THE  LIMITATIONS  OF  SCIENCE 


THE  LIMITATIONS 
OF  SCIENCE 


BY 


LOUIS  TRENCHARD   MORE,  PH.D. 

Professor  in  the  University  of  Cincinnati 


NEW  YORK 

HENRY   HOLT   AND    COMPANY 
1915 


COPYRIGHT,  1915, 

BY 
LOUIS  TRENCHARD  MORE 


Published  April,  1915 


THE   QUINN    *    BODEN    CO.    PRESS 
RAHWAY.   N.  J. 


Hypotheses  non  fingo.  Quicquid  enim  ex  phse- 
nomenis  non  deducitur,  hypothesis  vocanda  est;  et 
hypotheses  seu  metaphysics,  seu  physicae,  seu  qualita- 
tum  occultarum,  seu  mechanics,  in  philosophia  experi- 
mental! locum  non  habent.  In  hac  philosophia  proposi- 
tiones  deducuntur  ex  phsenomenis,  et  redduntur 
generales  per  inductionem. — NEWTON. 


46916.4 


PREFACE 

THE  separate  chapters  of  this  book  have  already 
been  published  as  essays  in  periodicals.  The  first,  sec- 
ond, third,  and  seventh  appeared  in  The  Hibbert  Jour- 
nal; the  fourth,  in  The  Philosophical  Magazine  and 
in  the  University  of  Cincinnati  Studies;  the  fifth,  in 
The  Monist;  and  the  sixth,  in  The  Unpopular  Review. 
But  they  have  been  rewritten  and  enlarged  so  as  to 
form  chapters  for  a  connected  discussion  of  the  Limita- 
tions of  Science.  This  was  not  a  difficult  task  since  I 
have  had  this  purpose  in  mind  from  the  beginning. 

CINCINNATI, 

December  2,  1914. 


CONTENTS 

CHAPTER  PAGE 

I    SCIENCE  AS  A  SYMBOL  AND  A  LAW      ..       .       i 

II    THE  METAPHYSICAL  TENDENCIES  OF  MODERN 

PHYSICS 32 

III  DESCARTES  AND  His  INFLUENCE  ON  RECENT 

SCIENCE 69 

IV  THE  SCIENTIFIC   METHOD      ....   107 
V    THE  CLASSICAL  AND  THE  NEW  MECHANICS  142 

VI    SKEPTICISM  AND  IDOLATRY  IN  SCIENCE  .       .   187 

VII     SCIENCE  AS  THE  ARBITER  OF  ETHICS       .       .  212 

INDEX 263 


THE    LIMITATIONS    OF    SCIENCE 

CHAPTER  I 
SCIENCE  AS  A  SYMBOL  AND  A  LAW 

Les  theories  contemporaines  sont  sur  ce  point  d'accord  avec 
1'histoire;  elles  consacrent  la  preponderance  dans  le  domaine 
scientifique,  de  1'hypothese  atomistique.— HANNEQUIN. 

IT  has  grown  to  be  an  axiom  in  modern  thought, 
that  the  hope  of  discovering  the  laws  of  nature  and 
our  relation  to  them  by  metaphysical  reasoning  is 
impossible.  The  term  metaphysical  reasoning  will  be 
used  consistently  to  mean  the  method  introduced  by  the 
Greek  philosophers  who,  however  they  might  differ 
in  minor  matters,  were  pretty  well  agreed  in  looking 
upon  what  we  call  nature  as  something  which  could  be 
investigated  subjectively;  that  is,  things  are  as  we  think 
them  to  be.  It  is  thus  directly  contrary  to  the  physical 
method,  which  maintains  natural  phenomena  and  laws 
to  be  entirely  objective  and  independent  of  our  thought ; 
according  to  this  method  no  theory  or  fact  can  be 
established  unless  it  is  completely  verified  by  experi- 
mental tests. 

So  little  in  the  long  years  since  Plato  and  Aristotle 
has  been  done  by  the  metaphysical  philosophers  to  add 


2      ;V*THK  IMITATIONS  -OF  SCIENCE 

to  our  positive  knowledge,  that  they  themselves  are 
abandoning  their  former  methods  for  that  of  the 
psychologist,  who  studies  even  the  faculties  and  the 
emotions  of  the  mind  objectively  by  means  of  the  phys- 
ical or  experimental  method.  Many  will  frankly  admit 
that  metaphysical  studies  are  chiefly  valuable  now  as 
a  history  of  the  development  of  thought,  and  agree 
with  Renan  that  "  Science,  and  science  alone,  can 
give  to  humanity  what  it  most  craves,  a  symbol 
and  a  law."  If  this  be  really  the  case,  if  the  attain- 
ment of  our  desire  for  an  accurate  and  real  knowledge 
of  our  environment,  its  phenomena  and  the  causes  of 
actions,  rests  with  science  alone,  then  it  becomes  neces- 
sary to  consider  whether  this  hope  also  must  prove  to  be 
fallacious.  Will  the  results  of  experiment  made  ob- 
jectively, which  must  however  be  interpreted  sub- 
jectively, fail  in  their  turn  as  criteria  of  truth? 

Of  the  various  sciences,  physics  offers  probably  the 
best  means  of  attacking  this  problem,  for  it  lies  be- 
tween the  concrete  classifications  of  the  natural  sci- 
ences, such  as  chemistry  and  biology,  and  the  abstract 
theories  of  pure  mathematics.  Physics,  on  the  one 
hand,  is  less  disturbed  by  the  multitude  of  details 
which  often,  in  the  natural  sciences,  prevent  the  grasp- 
ing of  a  central  idea;  while,  on  the  other  hand,  it  is 
more  circumscribed  than  mathematics  by  the  necessity 
of  constant  comparison  with  concrete  phenomena,  and 
so  avoids  the  danger  of  confounding  speculation  and 


SCIENCE  AS  A  SYMBOL  AND  A  LAW       3 

reality.  Thus  the  methods  of  physics  have,  to  a  degree, 
become  the  model  which  the  other  sciences  seek  to 
follow,  a  logical  mathematical  theory  based  on,  and 
corrected  by,  experimental  observation.  Moreover, 
this  science  presents  a  longer  and  more  consecutive 
history  than  most  of  the  others. 

It  is  also  noticeable  that  physics  treats  of  problems 
similar  to  those  of  metaphysics.  During  the  sixteenth, 
seventeenth,  and  eighteenth  centuries  philosophy  and 
physics  were  closely  united,  and  were  largely  domi- 
nated by  the  deductive  method,  which  was  introduced 
by  Descartes  and  which  led  to  persistent  attempts  to 
explain  scientific  laws  by  metaphysical  causes.  It  was 
then  that  the  two  great  metaphysical  ideas,  of  the  con- 
tinuity of  matter  with  its  identification  with  space,  and 
of  matter  as  a  form  of  indivisible  and  discrete  atoms 
different  in  kind  from  space,  were  adopted  as  scientific 
postulates,  and  were  expressed  in  mathematical  form. 
The  following  century  was  distinguished  by  a  separa- 
tion of  philosophy  and  physics,  as  that  period  is  best 
known  by  the  extraordinary  rise  of  the  experimental 
method  and  the  classification  of  phenomena  under 
mathematical  laws.  With  the  mass  of  experimental 
data  now  at  our  disposal,  an  imperative  need  is  again 
felt  for  theoretical  laws  which  shall  classify  them,  and 
accompanying  this  correct  scientific  need  there  is  a 
disposition  to  re-introduce  metaphysical  systems,  simi- 
lar in  aim  to  that  of  Descartes.  The  reason  for  this 


4  THE  LIMITATIONS  OF  SCIENCE 

change  in  method  in  the  nineteenth  century  is  under- 
stood if  we  consider  the  state  of  scientific  knowledge 
before  that  time. 

Few  of  the  properties  of  heat,  light,  sound,  and 
electricity  were  then  known,  but,  on  the  other  hand,  the 
laws  of  mechanics  were  well  established,  and  a  solid 
foundation  of  experimental  fact  permitted  a  broad 
and  comprehensive  application  of  pure  mathematics  to 
that  branch  of  physics.  It  is  altogether  natural  that 
mechanics  should  have  developed  first,  for  it  is  the  only 
part  of  the  science  which  rests  directly  on  the  data  of 
experience.  It  considers  only  material  bodies  and  their 
sensible  and  common  properties — such  as  the  occupa- 
tion of  space  and  the  resistance  to  motion.  To  measure 
properties  of  matter  other  than  spatial  and  dynamical 
requires  more  elaborate  apparatus,  and  it  is  more  diffi- 
cult to  separate  extraneous  accidents  from  such  at- 
tributes as  color,  temperature,  and  tone.  We  cannot, 
even  in  the  present  state  of  mathematical  knowledge, 
discuss  the  complex  processes  of  nature  as  they  are 
presented  to  us ;  for  example,  a  mathematical  law  which 
shall  define  all  the  changes  of  color,  of  electrical  in- 
tensity, etc.,  which  occur  when  a  body  is  heated,  is 
still  beyond  our  powers.  But  it  was  possible,  with  the 
knowledge  then  at  hand,  to  abstract  from  matter  all  its 
properties  except  that  of  a  simple  and  uniform 
space  and  force  attribute,  and  to  derive  a  theory  of 
mechanical  action  distinct  and  complete.  And  so  the 


SCIENCE  AS  A  SYMBOL  AND  A  LAW        5 

philosophical  scientists  of  the  French  revolutionary 
period,  with  whom  this  mechanistic  movement  cul- 
minated, had  only  mechanical  problems  to  work  on,  in 
which  their  knowledge  was  practically  as  accurate  as  it 
is  to-day. 

However  we  may  regard  the  effect  of  the  metaphys- 
ical system  of  Descartes  on  science,  there  can  be  only 
one  opinion  as  to  the  value  of  his  introduction  of  geom- 
etry into  physics.  By  it,  he  changed  medieval  natural 
philosophy  into  modern  physics.  When  he  discovered 
the  method  of  locating  the  position  of  any  point  by 
giving  its  distance  from  three  rectangular  straight 
lines,  he  made  it  possible  to  represent  the  path  of  any 
moving  body  by  a  geometrical  line  referred  to  the  same 
axes,  which  could  then  be  fully  defined  by  an  algebraic 
equation;  he  thus  made  it  possible  to  classify  all  mo- 
tions under  a  few  general  types,  and  so  founded  the 
science  of  kinematics.  For  example,  it  became  no 
longer  necessary  to  study  projectiles  individually,  for 
their  behavior  could  be  foretold  from  the  general  prop- 
erties of  parabolas.  Shortly  after  this,  Newton  and 
Leibnitz  invented  the  calculus,  which  enables  us  to  study 
moving  bodies  during  their  transit.  The  solution  of 
problems  of  continuous  motion  in  curved  lines  could 
never  be  satisfactorily  obtained  by  Euclidean  geometry, 
which  could  not  overcome  the  break  between  rest  and 
motion,  or  between  polygons  and  curves.  But  the 
application  of  the  infinitesimal  calculus  to  Cartesian 


6  THE  LIMITATIONS  OF  SCIENCE 

geometry  gives  us  a  solution  of  the  problem,  which, 
while  it  may  not  be  the  true  solution,  approximates  to 
the  truth  as  nearly  as  we  please.  This  is  accom- 
plished by  dividing  the  path  of  a  moving  body  into  sec- 
tions so  small  that  the  ratio  of  any  of  these  infinitesimal 
distances  to  the  time  necessary  to  traverse  it,  or  the 
velocity,  is  constant  and  finite.  Newton  had  discov- 
ered and  verified  the  law  of  universal  gravitation,  and 
had  also  collected  the  data  of  the  action  of  forces  on 
bodies,  and  embodied  them  in  three  laws  which  still 
serve  as  the  postulates  for  the  science  of  dynamics; 
and  D'Alembert  supplemented  them  by  a  general 
dynamic  law  of  the  motion  of  a  system  of  bodies 
acted  upon  by  forces  which  embraced  all  the  hitherto 
isolated  problems  of  this  character,  and  reduced  them 
to  a  special  and  simple  case  of  statics. 

On  the  theoretic  side,  Kant,  Lagrange,  and  others 
had  discussed  the  general  axioms  of  mechanics,  and 
had  established  the  three  fundamental  units — length, 
mass,  and  time;  and  it  is  generally  conceded  that  the 
solution  of  any  problem  of  mechanics  into  the  simplest 
combination  of  these  three  quantities  is  incapable  of 
further  reduction. 

But  one  thing  remained  before  an  imposing  structure 
could  be  raised  which  should  withstand  criticism,  and 
that  was  a  general  law  to  include  and  solve  problems 
relating  to  a  system  of  bodies  in  equilibrium  and  at 
rest.  And  Lagrange  accomplished  this. 


SCIENCE  AS  A  SYMBOL  AND  A  LAW       7 

Such  was  the  state  of  science  when  Laplace,  in  his 
Systeme  du  Monde,  and  Lagrange  in  the  Mecanique 
Analytique,  attempted  to  construct  a  theory  and  his- 
tory of  the  universe  by  means  only  of  the  general  and 
accepted  laws  of  the  two  mechanics:  celestial,  which 
concerns  the  heavenly  bodies,  and  terrestrial,  those  on 
the  earth.  Their  problem  has  been  stated  in  many 
ways,  but  this  may  serve : — Given  the  positions,  masses, 
and  forces  of  a  system  of  bodies  at  any  time,  to  find 
the  configuration  of  the  system  at  any  other  time,  previ- 
ous or  afterward. 

By  the  aid  of  the  principle  of  centers  of  inertia,  each 
celestial  body  could  be  replaced  by  a  mathematical 
point,  at  which  the  whole  mass  was  concentrated,  and 
endowed  with  a  force  of  attraction  according  to  New- 
ton's law  of  universal  gravitation.  In  a  similar  way 
each  terrestrial  body  was  divided  into  a  great  number 
of  small  elastic  particles,  or  atoms.  These  were  con- 
sidered to  be  invariable  and  indivisible,  and  they  were 
arbitrarily  endowed  with  the  same  force  of  universal 
gravitation,  acting  through  their  centers  of  inertia. 
This  force  could  be  assigned  to  these  imponderable 
masses,  separated  by  insensible  distances,  with  some 
probability  of  truth,  although  it  could  not  be  scien- 
tifically verified  by  experiment,  because  it  was  known 
to  be  a  property  of  ponderable  bodies  separated  by 
sensible  distances.  This  conception  of  matter  was 
generally  accepted,  as  the  original  atomic  theory  of 


8  THE  LIMITATIONS  OF  SCIENCE 

Democritus  had  been  extended  and  adapted  to  mathe- 
matical analysis  by  Gassendi,  Huygens,  and  Boscovich, 
Thus  all  bodies  and  systems  of  bodies  became  ab- 
stractly alike  in  character,  a  collection  of  mass  points 
acted  upon  by  an  attractive  force  common  to  all;  and 
if  the  state  of  the  universe  were  given  at  any  time,  it 
became  merely  a  problem  in  mechanics,  whose  laws  are 
fully  known,  to  find  its  history  from  the  beginning 
to  the  end.  As  Laplace  proudly  and  naively  answered : 
"  In  this  system  there  is  no  need  of  a  god."  Evidently 
this  statement  was  a  climax  of  materialism,  and  prob- 
ably can  never  again  be  uttered  with  such  assurance. 

So  solidly  was  this  theoretical  universe  built,  that  it 
defied  criticism  for  a  century,  and  finally,  as  it  seemed, 
established  science  on  a  mechanical  basis.  The  other 
branches  of  physics,  which  advanced  rapidly  during  the 
nineteenth  century,  fell  promptly  under  the  influence  of 
this  mechanistic  idea.  The  names  employed  show  this 
clearly.  We  have  the  wave  theories  of  light  and 
sound,  the  dynamic  theory  of  heat,  and  the  mechanical 
theories  of  electricity  and  magnetism.  In  all  these 
theories,  attributes  of  matter,  such  as  color,  tempera- 
ture, musical  pitch,  electrical  charge,  etc.,  are  ex- 
pressed by  the  mechanical  motions  and  forces  of 
atoms,  and  are  measured  solely  in  terms  of  the 
mechanical  units  of  length,  mass,  and  time.  The 
method  absolutely  eliminates  our  senses,  not  only  as 
instruments  capable  of  measuring  the  quantity  of  an 


SCIENCE  AS  A  SYMBOL  AND  A  LAW       9 

action,  but  even  denies  them  the  power  of  deciding 
qualitatively  between  phenomena;  for  the  light  which 
affects  the  eye,  the  sound  heard  by  the  ear,  and  the  heat 
perceived  by  temperature  are  essentially  the  same  thing, 
mere  variations  of  a  universal  force  of  gravitation. 
These  different  attributes  of  matter  are  scientifically 
identical  if  the  forces  involved  are  equal;  for  as  force, 
however  manifested,  was  held  to  be  a  mechanical  at- 
traction between  atoms,  all  these  quantities  can  be 
weighed  in  a  chemical  balance  and  have  no  essential 
difference.  While  there  may  have  been  great  diver- 
sity amongst  the  physicists  of  the  last  century  as  to  de- 
tails, there  was  but  this  one  explanation  of  nature: 
The  universe  was  a  complicated  machine,  whose  visible 
parts  were  connected  together  by  a  system  of  intangible 
links  called  atoms,  whose  complex  motions,  while  they 
might  defy  our  analytical  skill,  were  yet  completely 
expressible  by  general  mechanical  laws. 

To  find  the  weak  spot  in  this  mechanistic  theory, 
based  on  the  hypothesis  of  the  atom,  is  not  only  a  dif- 
ficult task,  but  is  one  which  ran  so  counter  to  the 
accepted  teachings  of  science  and  to  the  natural  preju- 
dices of  the  mind,  that  it  is  not  strange  if  most  men 
of  science  now  reason  as  though  the  atom  were  a 
matter  of  experimental  proof  rather  than  of  metaphys- 
ical speculation.  Such  a  mechanistic  theory  of  natural 
law  as  Lagrange  and  Laplace  evolved,  and  as  scientific 
thought  of  the  last  century  extended,  must  necessarily 


io          THE  LIMITATIONS  OF  SCIENCE 

depend  on  some  similar  atomistic  hypothesis.  Complex 
material  bodies  must  be  divided  up  into  elementary 
masses  so  small  that  any  conceivable  variation  in  them, 
except  mere  inertia,  must  be  forever  beyond  our  meas- 
urement or  even  conception.  Because,  if  the  atom 
were  divisible  or  variable,  which  its  very  name  denies, 
then  the  actions  of  its  component  parts  and  their  varia- 
tions might  be  productive  of  such  an  attribute  as 
temperature  or  color,  and  thus  introduce  into  the  atom 
properties  other  than  those  purely  mechanical. 

From  experience  we  know  of  only  one  way  a  tangible 
body  may  make  another  move,  and  that  is  by  a  direct 
push.  Either  atoms  must  be  granted  a  mysterious 
power  of  attraction  through  empty  space,  or  else  the 
part  of  the  universe  unoccupied  by  ponderable  matter 
must  be  filled  with  a  medium  or  ether,  to  act  as  the 
mechanical  link  between  atom  and  atom.  Now  this 
ether  is  either  continuous  or  discontinuous.  If  con- 
tinuous, it  would  serve  as  a  link ;  but  how  is  matter  to 
move  through  it  or  even  to  exist  in  it  unless  two  bodies 
may  occupy  the  same  space  at  the  same  time,  or  unless 
ponderable  matter  is  but  an  attribute  of  this  ethereal 
matter,  of  some  such  nature  as  a  whirlpool  on  the 
surface  of  water?  Such  a  variation  maintains  its 
identity  of  form  as  it  moves,  but  not  of  the  matter 
composing  it ;  this  is  to  replace  concrete  matter  by  the 
abstract  idea  of  form  or  motion,  which,  in  the  end,  is 
always  repugnant  to  our  sense  of  reality,  and  arouses 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      n 

the  impression  of  an  existence  in  a  world  of  dreams. 
On  the  other  hand,  if  the  ether  be  discontinuous,  it 
must  be  porous,  and  what  becomes  of  our  link  between 
atoms?  We  are  driven  to  the  creation  of  a  second 
more  tenuous  medium  to  fill  the  spaces  between  the 
grosser  one,  and  so  on  to  the  reductio  ad  absurdum 
pointed  out  by  Clifford. 

This  discussion  may  be  readily  summarized  in  two 
metaphysical  hypotheses  which  are  frequently  ac- 
cepted as  the  axioms  of  the  atomic  theory. 

First. — Given  the  masses  and  the  configuration  of 
the  centers  of  inertia  of  all  the  atoms,  with  the  law  of 
their  mutual  attraction,  then  all  the  attributes  of  mat- 
ter are  determined  and  the  problem  of  the  universe  is 
solved. 

Second. — As  a  visible  link  is  required  between  mov- 
ing parts  of  a  machine,  so  invisible  links,  called  ethers, 
multiplied  indefinitely,  must  exist  between  atoms. 

While  most  scientists  were  endeavoring  to  extend 
and  to  perfect  this  mechanical  theory,  there  were  a 
few  inclined  to  question  the  validity  of  the  axioms 
on  which  it  rested.  Among  the  latter,  Rankine  de- 
serves the  first  place.  In  a  memoir  read  before  the 
Philosophical  Society  of  Glasgow  in  1855,  he  discusses 
scientific  methods  in  general,  points  out  the  defects  and 
advantages  in  the  prevailing  theories,  and  outlines  a 
new  method  which  he  calls  the  science  of  energetics. 
His  criticism  is  of  the  highest  importance;  with  sub- 


12          THE  LIMITATIONS  OF  SCIENCE 

tile  irony  he  exposes  the  absurdity  of  a  materialistic 
theory  derived  from  mechanics  which  itself  inevitably 
rests  on  a  purely  metaphysical  basis. 

According  to  Rankine,  a  true  physical  theory  is  the 
most  simple  system  of  principles  from  which  the  formal 
laws  of  phenomena,  experimentally  discovered,  may  be 
deduced.  Such  a  theory  resembles  a  science  like 
geometry  in  that  it  originates  with  definitions  and 
axioms  for  first  principles,  and  derives  their  con- 
sequences logically,  by  propositions.  But,  in  general, 
a  physical  theory  differs  because  these  fundamental 
definitions  and  axioms  discovered  first  are  numerous 
and  complex,  since  they  are  deduced  from  the  mass  of 
facts  presented  to  us  immediately  by  nature;  whereas 
the  first  principles  and  axioms  of  geometry  are  few 
in  number  and  simple  in  character, — such  as  a  mathe- 
matical line  has  length  only, — and  are  the  results 
deduced  from  bodies  not  necessarily  real.  In  other 
words,  the  method  pursued  in  the  physical  theory  is 
inductive,  and  is  consequently  more  tentative  and 
laborious  than  the  deductive  method  of  geometry,  as 
the  acceptance  or  rejection  of  the  principles  derived 
must  depend  upon  their  agreement  with  facts  dis- 
covered gradually  by  observations,  and  not  upon  gen- 
eral properties  agreed  upon  once  for  all.  The  proposi- 
tions of  geometry  are  final,  if  the  axioms  and  defini- 
tions are  granted;  a  theory  of  physics  is  more  or  less 
conjectural,  as  its  first  principles  are  always  subject 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      13 

to  revision  because  of  the  discovery  of  new  phe- 
nomena. 

Two  methods  of  framing  a  physical  theory  may  be 
distinguished.  They  may  be  termed  the  abstractive  and 
the  hypothetical  methods. 

According  to  the  abstractive  method,  a  class  of  ob- 
jects or  phenomena  is  described  and  a  name  or  symbol 
assigned  to  that  assemblage  of  properties  common  to 
all  the  objects  or  phenomena  composing  the  class,  as 
perceived  by  the  senses,  and  without  introducing  any- 
thing hypothetical. 

There  is  only  one  example  of  a  complete  physical 
theory  formed  exclusively  from  the  data  of  experience 
by  the  abstractive  method, — the  principles  of  the  sci- 
ence of  mechanics.  The  objects  discussed  in  mechanics 
are  material  and  real  bodies,  all  of  which  possess  the 
sensible  properties  of  occupying  space  and  resisting 
change  of  motion.  The  phenomena  dealt  with  are 
confined  to  those  attributes  of  matter  distinguished  by 
the  words  force  and  motion,  which  we  have  found  to 
be  common  to  all  bodies  of  which  we  have  any  knowl- 
edge. And  the  laws  deduced  follow  from  axioms  and 
definitions  which  express  this  universal  experience. 

According  to  the  hypothetical  method,  the  existence 
of  a  class  of  fictitious  objects  or  phenomena,  which  can- 
not be  perceived  by  the  senses,  is  assumed.  And  prop- 
erties are  assigned  to  them,  similar  to  those  known  to 
be  true  of  a  class  of  real  objects  or  phenomena,  which 


14          THE  LIMITATIONS  OF  SCIENCE 

can  be  perceived  by  the  senses.  If  the  consequences 
of  such  a  hypothesis  are  afterwards  found  to  be  in 
agreement  with  the  results  of  observation  and  experi- 
ment, then  the  laws,  known  to  be  true  for  the  class  of 
real  objects  or  phenomena,  may  be  applied  to  the  hypo- 
thetical class.  The  objects  or  phenomena  considered 
by  this  method  are  thus  merely  matters  of  conjecture, 
and  their  nature  may  be  modified  at  any  time  so  as  to 
make  the  propositions  derived  from  them  conform  to  an 
expression  of  experimental  fact.  Such,  for  example,  has 
been  the  method  followed  in  the  wave  theory  of  light. 
To  explain  the  observed  action  of  light,  the  existence 
of  hypothetical  bodies,  called  atoms,  and  the  luminifer- 
ous  ether,  is  assumed,  and  properties  are  assigned  to 
them  similar  to  those  of  sensible  matter.  As  new 
phenomena  are  discovered  the  attributes  of  the  atom 
and  the  ether  are  modified  to  fit  the  requirements. 
This  theory  can  be  considered  only  as  a  convenient 
means  of  expressing  natural  laws,  and  is  always  sub- 
ject to  change,  as  it  does  not  depend  on  the  objective 
realities  fundamental  to  an  abstractive  method. 

Just  because  the  theory  of  the  mechanical  motions 
and  motive  forces  of  sensible  bodies  is  the  only  com- 
plete physical  theory,  and  because  it  does  not  require 
the  use  of  a  hypothetical  method  in  its  development, 
we  have  been  led  to  give  the  hypotheses,  advanced  as 
theories  in  the  other  branches  of  physics,  a  mechanical 
form.  The  classes  of  phenomena  considered  in  all 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      15 

these  theories  are  defined  conjecturally  as  being  due 
to  some  kind  of  mechanical  motion  and  motive  force, 
as  when  heat  is  defined  as  consisting  in  molecular  mo- 
tions, or  the  rigidity  of  solids  in  molecular  attractions 
and  repulsions. 

The  motions  and  forces  involved  in  these  theories 
can  no  longer  be  ascribed  to  sensible  matter,  but  either 
hypothetical  bodies,  such  as  the  luminiferous  ether,  or 
hypothetical  parts  of  real  bodies,  such  as  molecules, 
atoms,  ethereal  vortices,  or  other  imaginary  elements 
of  matter  must  be  created.  And  to  them  are  assigned 
properties  and  laws  resembling  as  closely  as  may  be 
those  of  sensible  bodies.  In  explaining  new  facts,  as 
they  are  discovered,  the  attributes  of  the  hypothetical 
matter  are  modified,  or  such  new  ones  assumed  as  may 
best  fit  the  case.  Such  mechanical  hypotheses,  not  be- 
ing based  on  experimental  evidence,  are  held  to  fulfill 
their  purpose  when  these  conjectural  attributes  explain 
in  the  simplest  and  most  plausible  way  the  largest 
body  of  known  phenomena  and  when  they  anticipate 
phenomena  afterwards  observed.  The  importance  and 
weight  of  these  hypotheses  increase  with  the  number  of 
phenomena  whose  laws  they  express. 

Certain  hypothetical  theories,  such  as  the  wave 
theory  of  light,  have  been  undoubtedly  useful,  since 
they  have  reduced  complicated  actions  to  a  few  simple 
laws.  And  also  they  tend  to  combine  all  branches  of 
physics  into  one  system  in  which  the  axioms  of 


16          THE  LIMITATIONS  OF  SCIENCE 

mechanics  are  the  first  principles  of  the  whole  science. 
But  they  must  be  employed  with  great  caution  and 
judgment.  Their  free  use  tends  to  confuse  the  essen- 
tial differences  between  hypothesis  and  fact,  between 
metaphysics  and  physics,  and  this  confusion  does  now 
exist  in  the  minds  of  the  public  generally  and  even  in 
those  of  many  men  of  science.  A  desire  is,  conse- 
quently, often  shown  to  explain  away,  or  set  aside, 
facts  inconsistent  with  a  preconceived  hypothesis. 

Such  is  briefly  Rankine's  criticism  of  the  prevailing 
mechanical  and  materialistic  theories  of  physics.  His 
conclusions  are  worthy  of  thoughtful  consideration. 
It  has  always  been  the  boast  of  science  that  by  its 
methods  we  may  avoid  the  pitfalls  in  which  meta- 
physical reasoning  inevitably  ends.  Now,  if  our  most 
elaborate  and  complete  scientific  theory  is  really  meta- 
physical, we  must  renounce  all  our  proud  claims  and 
consider  atomic  and  mechanical  theories  solely  on  the 
grounds  of  their  utility  and  simplicity. 

A  metaphysical  hypothesis,  valuable  solely  for  its 
utility,  is  always  dangerous,  for  by  constant  use  we 
tend  inevitably  to  give  an  objective  reality  to  things 
which  in  the  beginning  we  knew  to  exist  only  in  our 
own  minds.  And  this  tendency  is  especially  deplor- 
able in  science,  which  does  little  for  education  if  it  does 
not  recognize  clearly  the  limits  of  our  knowledge  and 
distinguish  accurately  between  reality  and  speculation. 

Now  the  belief  in  the  objective  reality  of  molecules, 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      17 

atoms,  ethers,  and  ethereal  vortices  has  grown  so 
steadily  that  little  objection  has  been  made  to  the 
recent  creation  of  a  whole  new  class  of  such  hypothet- 
ical objects,  called  indifferently  ions,  corpuscles,  elec- 
trons, or  particles,  which  are  assumed  to  be  the  con- 
stituent elements  of  the  hypothetical  atom.  Of  the 
three  classes  of  objects  it  is,  at  the  present  time,  the 
existence  of  the  sensible  bodies  which  is  in  danger 
of  repudiation.  This  is  the  case  not  only  in  the  minds 
of  the  thoughtless  but  in  those  of  the  leading  men 
of  science.  For  example,  Sir  J.  J.  Thomson,  in  the 
preface  to  his  Conduction  of  Electricity  Through 
Gases,  says :  "  The  possession  of  a  charge  by  the  ions 
increases  so  much  the  ease  with  which  they  can  be 
traced  and  their  properties  studied  that,  as  the  reader 
will  see,  we  know  far  more  about  the  ion  than  we  do 
about  the  uncharged  molecule."  Such  a  statement  is 
on  a  parallel  with  the  remark  made  to  me  by  another 
distinguished  physicist,  that  we  know  far  more  about 
the  ether  and  the  atom  than  we  do  about  sensible 
matter.  This  is  true,  and  in  the  same  way  as  a 
Frankenstein  might  say  of  a  mechanical  man  which 
he  had  conceived  and  constructed, — I  know  more  about 
him  than  I  do  about  a  real  man. 

Such  confusion  of  thought  is  directly  traceable  to 
the  fact  that  many  men  of  science  have  forgotten  the 
distinction  between  the  creations  of  nature  and  the 
creations  of  their  imaginations.  We  can  never  say 


i8          THE  LIMITATIONS  OF  SCIENCE 

more  of  molecules,  ions,  and  the  ether,  than  that  they 
may  exist;  but  ponderable  matter,  as  perceived  by  the 
senses,  has  an  objective  existence,  or  else  there  is  no 
place  for  science.  Since  Kant's  time  the  existence  or 
the  non-existence  of  those  insensible  links  in  the  uni- 
versal machine  is  known  to  be  equally  demonstrable; 
we  have  no  criterion  of  proof.  It  is  curious  that  we 
still  refuse  to  acknowledge  this.  If  we  look  askant 
at  Kant,  the  metaphysician,  we  have  only  to  turn  to 
Lagrange,  whose  scientific  claims  cannot  be  ignored, 
and  find  he  has  proved  by  rigid  mathematical  analysis 
that  any  phenomenon,  which  obeys  the  law  of  conser- 
vation of  energy,  is  capable  of  an  explanation  by  a 
mechanical  theory ;  but,  and  here  is  the  important  point, 
as  there  is  always  one  adequate  theory,  so  there  are 
also  an  indefinite  number  of  other  mechanical  theories 
which  will,  so  far  as  our  minds  are  concerned,  satisfy 
all  the  requirements  of  the  case.  We  have  no  criterion 
in  mechanics  by  which  we  may  determine  what  is  the 
actual  process  of  nature.  There  is  no  experimenium 
crucis,  and  we  choose  the  explanation  which  for  the 
moment  seems  to  be  the  simplest. 

Our  inability  to  decide  unequivocally  for  one  me- 
chanical hypothesis  instead  of  another  is  shown  also 
by  the  actual  history  of  physical  science.  Since  the 
time  of  Huygens  and  Newton  we  have  attempted  to 
settle  the  question  whether  light  is  due  to  a  wave 
motion  in  an  ether  or  to  small  particles  emitted  from 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      19 

luminous  bodies.  Many  times  it  has  been  announced 
that  the  question  has  been  decided  experimentally ;  for 
instance,  when  Foucault  found  that  the  velocity  of 
light  decreased  when  passing  through  transparent 
bodies,  instead  of  increasing  as  Newton's  hypothesis 
had  predicted.  But,  on  the  other  hand,  the  aberration 
of  light  discovered  by  Bradley  is  a  stumbling-block 
to  Huygens'  theory  and  is  a  simple  consequence  of 
Newton's.  Neither  of  these  experiments  caused  the 
abandonment  of  a  theory.  A  Newton  could  have 
altered  the  properties  of  the  corpuscle  and  a  Huygens 
is  sure  to  arise  who  can  alter  the  character  of  ethereal 
waves  so  as  to  explain  aberration;  in  fact,  it  has  been 
done  with  considerable  success  by  Sir  Joseph  Larmor. 
We  may  then  take  it  as  established,  both  on  theoretical 
and  on  historical  grounds,  that  no  experiment  has 
been,  or  will  be,  devised  to  decide  finally  between  the 
claims  of  the  two  hypotheses,  yet  the  corpuscular 
theory  was  abandoned.  The  reason  was  not  that  either 
was  impossible,  but  that  the  corpuscle,  with  the  accre- 
tions added  to  it  as  new  facts  were  discovered,  became 
too  unmanageable.  Huygens'  mechanical  wave  theory 
having  outgrown  its  usefulness  has  suffered  the  same 
fate.  He  ascribed  light  to  a  series  of  mechanical 
waves  propagated  through  an  elastic  ether,  but  the  at- 
tributes necessary  to  the  medium  became  so  contra- 
dictory that  a  new  theory,  advanced  by  Maxwell,  was 
accepted  as  a  great  relief.  In  this  theory,  the  ethereal 


20          THE  LIMITATIONS  OF  SCIENCE 

waves  are  not  mechanical  but  electro-magnetic,  similar 
to  those  we  now  use  in  wireless  telegraphy.  But  the 
difficulties  are  still  pursuing  us.  We  may  assume  that 
such  waves  can  pass  through  space,  but  we  cannot  con- 
struct a  mechanical  model  of  an  atom  or  ether  which 
will  produce  or  maintain  these  vibrations,  nor  have  we 
any  evidence  that  electro-magnetic  disturbances  can 
affect  the  optic  nerve  and  produce  the  sensation  of 
light.  The  prediction,  which  I  made  when  this  essay 
was  first  published,  that  we  shall  return  to  a  modified 
form  of  the  corpuscular  theory  with  the  electrified  par- 
ticle, the  constituent  of  the  atom,  as  an  agent,  has  been 
verified.  The  principle  of  relativity,  recently  an- 
nounced by  Professor  Einstein,  absolutely  requires  it. 

If  a  general  atomistic  theory,  which  seems  to  be  the 
only  practicable  hypothesis,  involves  these  inherent  dif- 
ficulties, and  if  it  presents  a  real  peril  to  correct  scien- 
tific thinking,  the  question  arises,  whether  some  general 
mechanical  explanation  of  all  physical  phenomena  is 
possible  which  is  not  so  limited. 

Rankine,  in  the  same  essay,  proposes  a  method  which 
he  calls  the  science  of  energetics.  As  we  have  been 
able  to  frame  with  some  success  a  theory  of  physics  by 
using  a  hypothetical  method,  we  should  have  even  more 
success  in  combining  all  the  branches  of  the  science 
into  one  general  theory  if  the  abstractive  method  were 
extended  and  applied  for  the  purpose.  Instead  of  sup- 
posing the  various  physical  phenomena  to  be  con- 


SCIENCE  AS  A  SYMBOL  AND  A  LAW     21 

stituted,  in  an  occult  way,  of  modifications  of  me- 
chanical motion  and  force,  let  us  attempt  to  frame  laws 
which  shall  embrace  the  properties  common  to  any  one 
class.  He  finds  energy,  or  the  capacity  to  effect 
changes,  to  be  the  common  characteristic  of  the  various 
states  of  matter  to  which  the  several  branches  of 
physics  relate.  If  then  we  frame  general  laws  regard- 
ing energy,  we  shall  be  able  to  apply  them,  with  appro- 
priate changes,  to  every  branch  of  physics. 

Rankine  evidently  denies  the  advisability  of  trying 
to  find  the  cause  of  the  attraction  of  bodies  for  one 
another,  or  the  mechanism  of  the  propagation  of  light 
and  heat  through  empty  space.  In  all  cases  we  have  a 
certain  quantity  of  energy,  acting  in  a  specific  manner. 
Our  aim  should  be  to  find  by  experiment  the  properties 
of  any  such  manifestation,  and  to  combine  all  common 
properties  by  general  mathematical  laws.  Such  was 
the  method  of  Newton  when  he  established  the  law  of 
universal  gravitation  and  refrained  from  publishing 
how  the  forces  of  attraction  could  act  through  space, 
and  no  discovery  has  aided  science  more.  But  after  he 
had  determined  experimentally  many  of  the  laws  of 
light,  he  advanced  the  hypothesis  that  these  phenomena 
were  caused  by  motions  of  intangible  corpuscles  and  he 
ventured  so  far  as  to  describe  the  shape  and  properties 
of  these  hypothetical  bodies.  It  is  claimed,  on  good 
grounds  apparently,  that  his  corpuscular  theory  retarded 
the  growth  of  the  subject  for  more  than  a  century,  by 


22          THE  LIMITATIONS  OF  SCIENCE 

preventing  the  adoption  of  the  temporarily  more  con- 
venient wave  theory. 

Whether  or  not  it  is  advisable  to  substitute  energy 
for  inertia,  or  mass,  as  the  general  attribute  of  matter 
which  will  best  serve  for  a  fundamental  unit,  may  be 
open  to  discussion.  But  it  seems  certain  to  me,  at 
least,  that  the  formulation  of  laws  deduced  mathe- 
matically from  experimental  data  alone,  and  not  con- 
jecture as  to  the  causes  of  phenomena,  is  the  true 
province  of  science  and  the  only  method  certain  not  to 
lead  us  into  vain  metaphysical  speculation. 

Unfortunately,  the  restraint  and  clarity  of  thought 
shown  by  Rankine  are  rare,  and  few  are  willing  to 
impose  limitations  on  speculation  or  to  forego  the  at- 
tempt to  create  a  subjective  and  metaphysical  scheme 
according  to  which  nature  shall  work.  In  the  hands 
of  his  successors,  notably  Mach,  Duhem,  and  Ostwald, 
these  barriers  were  cleared.  They  have  endeavored  to 
give  an  objective  reality  to  the  mathematical  equation 
of  energy.  To  make  an  entity  of  a  symbol,  to  speak 
of  centers  of  force  as  if  an  intelligible  image  were 
conveyed  to  the  mind,  to  make  matter  and  inertia  an 
attribute  of  energy,  is  even  more  metaphysical  than 
the  concepts  of  atoms  and  ethers,  which  could,  at  least, 
be  likened  to  sensible  objects.  With  Professor  Ost- 
wald, the  most  militant  defender  of  the  science  of 
energetics,  matter  disappears  altogether;  empty  space 
is  known  to  us  only  by  the  quantity  of  energy  necessary 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      23 

to  penetrate  it,  and  occupied  space  is  merely  a  group 
of  various  energies.  In  his  enthusiasm  he  does  not 
hesitate  at  difficulties.  "  When  a  stick  strikes  you," 
he  exclaims,  "  which  do  you  feel,  the  stick  or  the 
energy  ?  "  One  might  as  well  ask  the  old  question, 
Which  comes  first,  the  owl  or  the  egg? — a  matter  of 
infinite  dispute  and  no  decision.  Although  Professor 
Ostwald's  work  bristles  with  mathematical  equations 
and  scientific  terms,  he  asks  us  to  return  to  the  meta- 
physical methods  of  the  medieval  schoolmen — to  thrash 
over  again  the  endless  verbal  disputes  of  nominalists 
and  realists. 

While  mechanics  is  the  only  branch  of  physics  which 
has  become  a  complete  science  through  the  use  of  the 
inductive,  or  abstractive,  method,  just  as  soon  as  we 
invent  atoms  and  ethers,  or  consider  an  abstract  quan- 
tity, like  energy,  to  be  an  entity,  in  order  to  explain 
the  modus  operandi  of  matter  and  motion,  and  to  serve 
as  connecting  links  in  explaining  non-mechanical 
phenomena,  such  as  electricity  and  light,  mechanics 
drifts  at  once  into  a  highly  metaphysical  and  subjective 
study  where  each  man's  opinion  is  guided  only  by  an 
inward  sentiment  of  knowledge.  To  what  lengths 
this  can  go,  I  shall  show  in  a  later  chapter  when  I 
present  the  confusion  of  thought  of  certain  eminent 
men  of  science  who  change  impersonal  mechanical 
energy  into  a  kind  of  vital  and  beneficent  principle 
ruling  over  the  thoughts  and  actions  of  human  society, 


24          THE  LIMITATIONS  OF  SCIENCE 

or  of  Sir  Oliver  Lodge,  who  bestows  on  the  ether  the 
ability  to  carry  ghostly  messages  as  well  as  light. 

As  a  critical  attempt,  the  school  of  energetics  has 
done  good  work  by  calling  attention  to  the  inadequacies 
of  atomic  theories,  yet  as  a  positive  method  it  has  had 
comparatively  little  effect  until  very  recently,  when  it 
has  been  pushed  by  a  school  of  German  physicists  into 
what  can  only  be  called  an  abyss  of  confusion  where, 
as  in  a  sort  of  looking-glass  world,  all  things  tan- 
gible become  intangible  and  the  abstract  replaces 
the  concrete.  But  the  majority  of  men  of  science  still 
rely  absolutely  on  atomic  hypotheses.  Indeed,  a  fresh 
stimulus  has  been  given  them  by  the  efforts  to  explain 
the  experimental  facts,  recently  discovered,  concerning 
Roentgen  rays,  the  passage  of  electricity  through  gases, 
and  the  properties  of  radium;  facts  which  will  probably 
do  more,  in  the  end,  to  discountenance  mechanical 
models  of  phenomena,  by  making  them  practically  un- 
manageable, than  the  theoretical  criticisms  of  the  fol- 
lowers of  the  school  of  energetics. 

So  long  as  the  hypothesis  of  an  invariable  and  in- 
divisible atom  gave  a  reasonably  simple  and  satisfac- 
tory method  of  attacking  the  problems  of  physics, 
even  those  men  of  science  who  were  ready  to  acknowl- 
edge the  tentative  character  of  the  hypothesis  and  the 
contradictory  nature  of  its  postulates  were  unwilling 
to  try  other  methods.  But  the  phenomena  mentioned 
above  do  not  fit  into  the  general  scheme,  because  the 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      25 

mechanical  atom  does  not  explain  such  electrical 
phenomena,  unless  we  arbitrarily  associate  with  it  other 
supposititious  electrical  fluids  or  else  give  it  complex 
and  variable  electrical  attributes;  both  of  which  defeat 
the  purpose  of  explaining  all  phenomena  by  means  of 
a  single,  invariable  entity.  Their  explanation  thus  re- 
quires us  either  to  abandon  the  atomic  theory  or  to 
modify  it  radically;  the  latter  has  been  done,  and  the 
atom  is  now  supposed  to  be  a  complex  body  composed 
of  an  aggregation  of  invariable  and  indivisible  par- 
ticles, called  electrons. 

As  might  be  supposed,  some  specious  advantages 
have  been  obtained.  The  chemists  have  long  sought  in 
vain  for  a  chemical  element  whose  atom  might  be  con- 
sidered the  primordial  substance,  and  from  which  the 
atoms  of  the  other  elements  were  derived.  This  new 
idea  of  the  atom  offers  a  solution,  for  the  chemists  may 
now  construct  the  atoms  of  all  the  elements  out  of  dif- 
ferent combinations  of  corpuscles.  Also  the  early 
investigators  in  electricity,  as  Franklin  and  Du  Fay, 
were  led  to  postulate  the  existence  of  subtile  electric 
fluids  to  explain  the  fact  that  electrified  matter  some- 
times showed  a  force  of  attraction  and  sometimes  of 
repulsion.  Later,  in  the  theories  of  Faraday  and 
Maxwell,  the  hypothesis  of  fluids  was  abandoned 
and  the  ends  of  the  atom  of  matter  were  endowed 
respectively  with  the  properties  of  electrical  attrac- 
tion and  repulsion.  Now  it  is  possible  to  discard  this 


26          THE  LIMITATIONS  OF  SCIENCE 

variability  in  the  simple  atom  by  supposing  some  of  the 
corpuscular  elements  of  a  complex  atom  to  exhibit  the 
one  kind  of  electric  force,  and  others  the  opposite 
kind. 

In  spite  of  these  advantages  and  others  which  might 
be  cited,  the  prime  fact  remains  that  it  is  now  neces- 
sary to  abandon  the  historic  and  hitherto  invincible 
atomic  theory  for  another  which  is  still  more  conjec- 
tural. For  the  former  element  of  matter,  simple  in 
nature,  we  have  substituted  another,  complex  in  char- 
acter, and  have  thereby  given  up  the  chief  and  to  many 
the  only  value  of  an  atomic  theory. 

The  corpuscular  theories  advanced,  almost  simul- 
taneously by  Lorentz  and  Larmor,  show  this  clearly. 
Sir  Joseph  Larmor,  in  his  treatise  on  JEther  and 
Matter,  presents  a  view  of  the  constitution  of  matter 
which  is  sufficient  over  an  extensive  range  of  physical 
theory,  and  which  he  trusts  will  not  be  made  more 
complex  until  it  proves  inadequate  in  some  definite 
feature.  According  to  his  hypothesis,  the  atom  of  mat- 
ter is  composed  of  a  system,  probably  large  in  number, 
of  positively  and  negatively  electrified  protions  (called 
frequently  by  others  corpuscles,  electrons,  or  ions) 
in  Estate  of  steady  orbital  motion  around  each  other. 
The  passage  of  electricity  through  a  conductor  or  from 
one  body  to  another"  is  effected  by  a  transference  of 
electrically  charged  pVotions  from  one  atom  to  another. 
The  differences  in  the  chemical  elements,  such  as  iron 


SCIENCE  AS  A  SYMBOL  AND  A  LAW     27 

or  hydrogen,  can  be  accounted  for  by  ascribing  them 
to  various  aggregations  of  the  protions.  As  for  the 
protions  themselves,  they  are  in  whole  or  part  nuclei 
of  intrinsic  strain  in  the  ether,  places  where  the  con- 
tinuity of  this  medium  has  been  broken  and  cemented 
together  again. 

Such  a  theory  is  evidently,  and  in  the  highest  degree, 
artificial  and  metaphysical,  and  Sir  Joseph  Larmor 
would  be  the  last  to  assert  that  he  has  given  a  true 
picture  of  the  constitution  of  matter.  Its  value  must 
rest  on  the  belief  that  it  is  the  simplest  theory  avail- 
able for  explaining  experimental  facts.  But  the  diffi- 
culties inherent  to  the  theory  are  insuperable.  It  is 
almost  inconceivable  that  our  simplest  idea  of  the  ulti- 
mate constituent  of  the  chemical  element  should  be  an 
/ 

atom,  so  bewilderingly  complex  in  character.  Each 
atom  of  an  apparently  quiescent  body  is  itself  an 
aggregation  of  particles,  vastly  more  intricate  than  the 
stellar  systems,  and  whirling  around  each  other  with  a 
motion  approximating  a  hundred  thousand  miles  per 
second.  And  although  the  atom  itself  still  possesses 
the  attributes  of  matter,  its  constituents  become  merely 
nuclei  of  strain  in  the  ether.  What  must  be  the 
structure  of  an  ether  which  can  maintain  such  a  com- 
plex of  strains  as  all  the  countless  atoms  in  the  uni- 
verse would  require?  If  we  can  never  be  sure  matter 
is  actually  so  constituted,  it  is  unfortunate  to  create 
a  world  so  counter  to  our  instinctive  belief  that  in  a 


28          THE  LIMITATIONS  OF  SCIENCE 

correct  definition  a  complex  idea  must  be  explained  into 
simpler  parts. 

The  theory  of  Professor  Lorentz  is  essentially  the 
same,  although  he  does  not  attempt  any  speculations 
as  to  the  structure  of  the  ether  or  atom.  But  he,  too, 
postulates  the  existence  of  small,  electrically  charged 
particles  in  all  bodies  and  deduces  all  electrical  laws 
from  the  positions  and  motions  of  these  electrons. 

It  is  not  necessary  to  state  that  both  these  writers 
develop  their  theories  with  great  skill  and  from  a  pro- 
found knowledge  of  the  science.  They  have,  perhaps, 
achieved  a  closer  unity  in  the  branches  of  physics, 
although  I  feel  confident  that  they  have  really  only 
substituted  an  electrical  atom  which  will  not  explain 

I  matter  for  a  material  atom  which  would  not  explain 
electricity.  And  to  attain  this  ambiguous  advantage 
they  have  introduced  postulates  which  lie  still  further 
outside  the  domain  of  science  and  have,  by  fixing  our 
attention  on  a  sub-atom,  given  an  appearance  of  greater 
reality  to  the  relatively  gross  atom. 

The  influence  of  such  abstruse  and  metaphysical 
theories  on  scientific  thought  is  already  apparent  in  a 

I  certain  eagerness  to  advance  startling  hypotheses  and 
novel  ideas.  Many  men  of  science  of  to-day  have  tem- 

\  porarily  put  aside  the  sobriety  and  restraint  which 
should  characterize  scientific  reasoning.  The  most 
tremendous  results  are  based  on  insufficient  evidence, 
and  the  simple  statement  that  the  cause  of  a  phenom- 


SCIENCE  AS  A  SYMBOL  AND  A  LAW      29 

enon  is  to  be  found  in  electronic  action  is  considered 
satisfactory.  Physicists  in  Germany  are  gravely  dis- 
cussing whether  electrons  are  spheres  or  discs  in  shape. 
The  transmutation  of  the  elements,  a  problem  which 
has  baffled  research  for  centuries,  is  announced  as  an 
assured  fact,  because  radium  and  a  few  other  sub- 
stances spontaneously  give  off  energy.  Electricity  is 
declared  to  be  a  substance  and  matter  is  said  to  be  not 
a  substance,  but  an  attribute  of  electricity,  because  an 
electrified  body  has  an  apparent  increase  in  its  resist- 
ance to  motion;  although  we  know  nothing  about  the 
nature  of  either  matter  or  electricity.  Others  say  that 
the  universe  is  a  sort  of  modified  ether;  although  we 
never  can  have  cognizance  of  an  unmodified  ether. 
Surely  matters  of  such  infinite  difficulty  and  of  such 
supreme  importance  should  not  be  decided  before  the 
most  rigid  elimination  of  more  natural  causes.  The 
fact  is,  all  such  statements  as  these  are  merely  words 
which  convey  no  ideas;  the  problems  involved  are 
entirely  beyond  our  powers  of  solution  either  by 
physical  or  by  metaphysical  methods.  Such  confusion 
of  thought  and  dissolution  of  the  boundaries  between 
fact  and  fancy  are  deplorable,  and  if  they  create  trouble 
in  the  minds  of  scientific  men,  they  have  absolutely 
bewildered  the  general  public.  Books  of  a  popular  na- 
ture are  constantly  appearing  which  change  these  re- 
sults of  speculation  into  established  fact,  and  their 
readers  naturally  credit  the  most  astounding  state- 


30          THE  LIMITATIONS  OF  SCIENCE 

ments.  The  day  may  come  when  a  new  war  will  arise 
between  science  and  religion  on  the  issue  that  the  de- 
ductions of  science  are  too  metaphysical  to  be  of  value. 

It  may  be  necessary,  when  the  laws  and  phenomena 
of  a  science  are  vaguely  known,  to  employ  a  hypothet- 
ical method.  And  a  hypothesis  may  then  be  of  great 
use  in  creating  a  certain  unity  amongst  diverse  ele- 
ments. But  the  question  may  well  be  asked,  whether 
physical  science  has  not  outgrown  a  method  proper  for 
the  alchemist  and  the  astrologer. 

The  attempt  to  unite  the  phenomena  of  all  branches 
of  physics  in  a  few  general  laws  and  to  explain  their 
cause  by  the  aid  of  atoms  has  engaged  the  attention 
of  the  greatest  men  of  science  for  more  than  a  century. 
They  have  spent  upon  these  problems  infinite  thought 
and  pains,  and  in  the  end  we  have  a  body  of  laws  firmly 
established  on  experimental  evidence,  but  the  causes  of 
these  laws  are  as  hopelessly  obscure  as  ever.  The 
atom  has  failed  to  satisfy  the  requirements,  and  now 
the  electron  is  added  to  explain  new  facts,  an  hypothesis 
on  an  hypothesis.  As  our  knowledge  increases,  who 
can  doubt  but  that  these,  in  their  turn,  will  give  place  to 
others  still  more  complex,  if  the  same  method  is  pur- 
sued, until  the  succession  of  atoms  and  sub-atoms  will 
make  the  whole  atomistic  idea  an  absurdity  ? 

Just  as  we  have,  after  centuries  of  incessant  con- 
troversy, been  forced  to  accept  the  fact  that  we  cannot 
by  reasoning  from  our  consciousness  obtain  an  ob- 


SCIENCE  AS  A  SYMBOL  AND  A  LAW     31 

jective  knowledge  of  natural  causes,  so  we  must  come 
to  realize  that  reasoning  from  experimental  evidence  is 
subject  to  exactly  the  same  limitations.  Science,  in 
other  words,  like  philosophy,  has  no  ontological  value. 
Should  not  the  men  of  science  clearly  recognize  this 
fact,  and  confine  their  effort  to  the  legitimate  function 
of  science — the  discovery  of  natural  phenomena  and 
their  classification  into  general  laws  derived  by  logical 
mathematical  processes  ? 


CHAPTER  II 

THE  METAPHYSICAL  TENDENCIES  OF 
MODERN  PHYSICS 

Pero,  signer  Simplicio,  venite  pure  con  le  ragioni  e  con  le 
dimostrazioni  vostri  o  di  Aristotile,  e  non  con  testi  e  nude 
autorita,  perche  i  discorsi  nostri  hanno  a  essere  intorno  al 
mondo  sensibile,  e  non  sopra  un  mondo  di  carta. — GALILEO. 

IT  is  a  more  or  less  simple  thing  to  discover  and 
follow  the  main  current  of  thought  in  a  science  like 
physics,  which  must  develop  logically  or  not  at  all, 
after  the  confusion  of  strife  has  passed  away  and  only 
the  permanent  additions  to  our  knowledge  remain. 
This  has  been  attempted  in  the  former  chapter,  so  far 
at  least  as  the  atomic  theory  is  concerned.  It  was 
then  shown  that  if  we  build  up  a  homogeneous  hypoth- 
esis of  the  natural  phenomena — heat,  light,  sound,  and 
electricity — from  an  analogy  to  mechanical  laws,  we 
inevitably  postulate  the  objective  existence  of  matter, 
and  create  a  series  of  fictitious  ethers,  and  of  atomic,  or 
indivisible,  elements  of  matter.  The  claim  was  also 
made  that  this  method  which  attempts  to  explain  the 
laws  of  nature  not  only  fails  to  do  so,  but  also  pre- 
vents the  adoption  of  a  better  scientific  procedure. 

In  the  first  place,  it  is  difficult  to  point  to  any  scien* 

32 


TENDENCIES  OF  MODERN  PHYSICS       33 

tific  discoveries  directly  and  inevitably  produced  by  a 
specific  atomic  theory.  The  contrary  of  this  opinion 
is  very  generally  held,  and  many  such  discoveries  in 
chemistry  and  physics  are  laid  at  its  door.  The 
chemist  searches  for  and  combines  new  compounds 
of  the  elements,  and  bases  his  theory  on  the  assump- 
tion that  each  element  is  disintegrable  only  to  a  fixed 
atom.  But  this  means  nothing  more  than  to  say  that 
the  elements  combine  in  definite  proportions  of  mass, 
and  consequently  does  not  bear  on  the  question  whether 
matter  is  infinitely  divisible.  The  chemist  would  have 
been  driven  to  the  same  laws  of  chemical  combina- 
tion if  he  had  believed  matter  to  be  infinitely  divisible. 
This  statement  is  true,  because  chemical  analysis  and 
synthesis  progress  imperturbed  and  as  rapidly  now 
when  the  chemical  atom  is  supposed  to  be  decompos- 
able. And  the  same  was  true  of  chemical  progress 
before  Dalton  proposed  his  atomic  theory,  which  be- 
sides was  so  simple  in  form  as  to  be  little  more  than 
the  generalization,  that  from  experience  we  may  say 
chemical  substances  unite  in  simple  multiples  of  a  unit 
chemical  mass,  called  the  atom,  instead  of  simple  pro- 
portions of  mass.  That  is,  Dalton's  atomic  theory  was 
more  closely  related  to  the  abstractive  than  to  the 
hypothetical  method  and  really  has  little  in  common 
with  the  physical  atomic  hypothesis  which  gives  defi- 
nite and  complex  functions  to  the  atom.  As  examples 
in  another  field,  we  find  the  phenomena  and  laws  of  the 


34          THE  LIMITATIONS  OF  SCIENCE 

double  refraction  and  polarization  of  light  were  dis- 
covered by  Huygens  before  he,  and  later  Fresnel, 
attempted  to  explain  them  as  a  modification  of  me- 
chanical waves  in  an  elastic  solid  ether;  and  Newton 
announced  the  laws  of  the  interference  of  light  which 
occurs  when  there  are  reflections  between  thin  films 
before  he  pictured  this  phenomenon  by  his  hypothesis 
of  corpuscles.  To-day  all  these  laws  remain  while  the 
specific  hypotheses  have  been  discarded.  How  can  we 
say  the  hypothesis  of  atoms  and  ether  led  to  dis- 
covery in  these  cases?  The  fact  is  just  the  contrary: 
hypothesis,  at  least  that  part  of  it  which  consists  in 
developing  a  mechanical  model  of  the  action,  follows 
experimental  discovery;  it  is  the  effort  to  explain  or 
visualize  the  unknowable  processes  involved  in  known 
experimental  facts  and  mathematical  laws. 

In  the  second  place,  these  metaphysical  hypotheses 
progress  from  the  simple  to  the  complex.  Each  new 
fact  discovered  adds  its  quota  to  the  irreconcilable  and 
conflicting  properties  of  the  ether  and  the  atom,  and 
these  invisible  links  of  the  universal  machine  grow 
more  and  more  bewildering  and  complicated,  until  the 
whole  construction  falls  to  pieces.  Nor  is  this  all ;  the 
man  of  science  forgets  that  he  is  building  toy  houses, 
and  ends  by  believing  in  their  reality.  Even  if  hypoth- 
esis does  not  carry  him  so  far,  it  certainly  has  this 
effect  on  others  who  accept  the  dogmas  of  science 
without  discrimination.  It  is  no  small  danger  thus  to 


TENDENCIES  OF  MODERN  PHYSICS       35 

confuse  reality  and  imagination;  a  science,  which  be- 
comes so  hypothetical  or  so  specialized  as  to  be  unin- 
telligible to  the  educated  man,  is  apt  to  become  as  sterile 
as  a  religion  which  is  in  the  sole  possession  of  a  hier- 
archy. 

This  excessive  use  of  hypothesis  has  developed  a 
sort  of  scientific  cult  which  somewhat  resembles  a 
religious  dogma,  in  that  adverse  criticism  of  either 
arouses  a  feeling  of  personal  irritation.  The  rancor  of 
religious  polemic  is  well  known  and  is  said  to  be  due 
to  the  fact  that  the  believer  of  a  religion  relies  on  re- 
vealed truth,  to  doubt  which  is  sinful.  The  same  oc- 
curs with  the  supporters  of  a  scientific  hypothesis,  who 
declare  their  system  to  be  founded  on  objective,  experi- 
mental fact,  and  to  be  developed  by  logical  methods, 
so  that  in  doubting  the  hypothesis  we  are  sinning 
against  truth  and  reason, — the  gospels  of  science.  On 
the  other  hand,  discussions  in  experimental  science  are 
noted  for  their  calmness,  for  then  we  are  criticising, 
not  personal  opinions  but  objective  facts,  and  we  care 
comparatively  little  which  way  the  matter  ends.  The 
theorist,  on  the  contrary,  forgets  that,  while  founded 
on  experience,  his  hypothesis  is  developed  in  one  way 
or  another  according  to  his  own  personal  opinion; 
for  example,  the  same  facts  of  light  made  Newton 
believe  in  corpuscles  and  Huygens  in  waves,  and  so 
the  theorist  injects  into  his  discussions  the  bitterness 
of  personal  defeat  or  the  exultation  of  personal  victory. 


36          THE  LIMITATIONS  OF  SCIENCE 

There  is  yet  another  purpose  in  science  which  re- 
quires simplicity  instead  of  complexity.  Physics,  to  be 
something  more  than  an  intellectual  puzzle  for  the 
specialist,  should  enlarge  our  power  over  the  external 
world  and  increase  our  use  of  natural  resources.  Con- 
sider how  great  an  advance  we  might  make  in  this 
direction  if  hypothesis  and  occult  causes  were  reduced 
to  a  minimum.  Instead  of  a  mass  of  abstruse  specu- 
lations on  the  nature  of  ether  and  matter,  our  treatises 
might  present  a  clear  and  logical  discussion  of  natural 
phenomena  and  their  laws.  The  work  of  Lord  Kelvin 
is  typical.  He  has  interspersed  in  his  writings  probably 
a  score  of  models  of  the  atom :  now  it  is  a  vortex  or 
whirlpool  in  a  continuous  fluid  ether ;  now,  a  box  con- 
taining gyrostats  or  wheels  spinning  on  axes ;  again,  it 
is  a  complicated  structure  of  balls,  strings,  and  springs. 
No  two  of  these  agree  in  principle,  and  at  best  repre- 
sent crudely  a  limited  number  of  the  properties  of 
matter  and  fail  for  others.  Is  there  not,  after  all, 
something  almost  pathetic  in  this  incessant  striving 
of  the  greatest  physicist  of  our  times  after  the  un- 
knowable, building  card  houses  which  must  be  knocked 
down  to  provide  material  for  new  ones?  Certainly 
more  of  his  great  and  permanent  constructive  work 
would  be  the  property  of  the  world  if  we  had  neglected 
his  hypotheses  and  developed  more  diligently  his  ex- 
periments and  his  laws. 

On  the  other  hand,  it  is  a  serious  matter  to  try  to 


TENDENCIES  OF  MODERN  PHYSICS       37 

sweep  aside  so  large  a  part  of  scientific  thought  as 
hypothesis  has  been,  unless  it  is  really  parasitical, — a 
hindrance  rather  than  an  aid  to  development.  This 
opinion  as  to  the  uselessness  of  hypothesis  seems  to  be 
gaining  ground.  Thus  M.  Duhem,  in  his  Theorie 
Physique,  states  that  physical  theories  must  have  one 
of  two  aims:  either  to  explain  laws  which  have  been 
established  from  experience,  or  to  classify  such  laws 
without  giving  any  explanation.  Of  the  two,  the  sec- 
ond only  is  a  legitimate  scientific  process,  as  the  first 
method  makes  physics  dependent  on  metaphysics  and 
so  introduces  occult  and  unverifiable  causes.  A  proper 
theory  should  thus  give  us  a  classification  of  laws 
and  should  point  to  new  experimental  methods,  thereby 
tending  to  intellectual  economy  in  that  we  are  per- 
mitted to  forget  a  multitude  of  details  and  otherwise 
isolated  facts  in  one  common  expression.  He  further 
claims  that  the  construction  of  a  mechanical  model 
as  an  explanation  of  a  law  does  not  lead  to  such  dis- 
coveries, since  these  are  really  derived  from  abstract 
principles,  the  model  being  invented  afterwards  merely 
to  make  the  law  concrete.  In  this  opinion  he  is  sup- 
ported by  Hertz,  who,  after  discovering  experimentally 
the  electric  waves  predicted  by  Maxwell,  found  the  best 
statement  in  Maxwell's  equations,  and  not  in  his  model 
of  ethereal  lines  of  force. 

A  ruthless  and  complete  elimination  of  hypothesis  is 
undoubtedly  impossible,  and  is  not  even  desirable.    We 


38          THE  LIMITATIONS  OF  SCIENCE 

tend  invariably  to  express  our  abstract  conclusions  in  a 
more  or  less  concrete  form.  We  shall  always  speculate 
about  the  manner  of  the  propagation  of  light  to  the 
earth  from  the  sun,  and  it  is  convenient  to  express  this 
transfer  of  energy  either  as  a  periodic  disturbance 
taking  place  in  something  filling  space  or  as  something 
projected  through  space.  Such  indefinite  speculations 
are  simple  enough  and  allow  us  to  state  all  that  we 
need  in  order  to  assume  continuity  of  action  in  free 
space.  The  obscurity  and  confusion  in  the  science  of 
optics  arise  from  the  attempts  to  express  in  detail  the 
nature  of  the  waves  or  of  the  particles  of  light.  A 
method  where  speculation  is  kept  to  its  lowest  terms  is 
quite  different  from  the  prevalent  custom  of  spending 
the  greater  part  of  our  effort  on  the  fictitious  proper- 
ties of  the  ether  rather  than  on  the  phenomena  and 
laws  of  matter. 

The  problem  of  tracing  the  tendencies  of  thought 
concealed  in  the  conflicting  data  and  opinions  of  the 
present  state  of  physics  is  difficult,  and  this  difficulty 
is  increased  by  the  unusual  amount  of  new  material 
brought  to  light  since  the  discovery  of  the  X-rays  by 
Professor  Roentgen  in  1895.  The  phenomena  con- 
nected with  the  discharge  of  electricity  through  gases 
and  with  radio-activity  are  obscure,  and  speculation 
about  them  correspondingly  bold.  There  is  a  desire, 
quite  common,  to  ignore  the  importance  of  the  more 
regular  advance  in  other  branches  of  physics  and  to 


TENDENCIES  OF  MODERN  PHYSICS       39 

assume  that  the  new  methods  of  attack  which  have 
arisen  are  essentially  different  from  the  thoughts  and 
speculations  of  former  physicists  and  not  subject  to 
their  failure.  This  idea  is  brought  out  by  Mr.  Camp- 
bell in  his  recent  book  on  Modern  Electrical  Theory, 
when  he  contrasts  the  work  of  Faraday,  about  1830, 
and  his  predecessors  with  that  of  living  physicists: 
"  Men  of  his  own  and  of  the  preceding  era  had  founded 
'natural  philosophy';  they  had  made  discoveries  and 
had  elaborated  theories  which  still  form  part  of  the 
frame-work  of  the  physical  sciences.  But  their  work 
has  little  interest  for  us  to-day.  Their  aims,  their  con- 
ceptions, their  whole  attitude  toward  the  problems 
which  they  investigated  differ  so  widely  from  our  own, 
that,  while  their  results  may  be  the  basis  of  modern  re- 
search, their  methods  afford  little  inspiration  for  it." 
This  is  far  from  being  the  case;  if  we  can  assign 
definite  periods  to  so  continuous  a  development  as  the 
history  of  science  has  shown,  we  should  certainly  date 
modern  physics  from  the  seventeenth  century  when 
Galileo  introduced  experimental  methods  and  Des- 
cartes applied  analytical  geometry  to  physics:  human 
thought  does  not  progress  at  this  late  day  by  cutting 
loose  from  the  past ;  especially  when  that  past  is  said 
to  date  from  the  middle  of  the  nineteenth  century. 
Where  the  "  new  views  "  are  not  merely  statistical 
observations  or  fugitive  models  of  some  particular 
phenomenon — that  is,  where  there  is  a  philosophical 


40          THE  LIMITATIONS  OF  SCIENCE 

background  to  our  recent  work — we  have  abandoned 
the  ideas  of  the  atomistic  school  of  the  nineteenth  cen- 
tury only  to  fall  back  on  the  doctrines  formulated  by 
Descartes  in  the  seventeenth,  as  Sir  Joseph  Larmor  has 
pointed  out. 

To  show  this  connection,  it  is  necessary  only  to  out- 
line and  contrast  briefly  these  two  methods  of  scientific 
procedure  now,  as  I  have  already  shown  the  tendencies 
of  the  atomistic  school  and  shall  give,  in  the  next  chap- 
ter, the  ideas  of  Descartes.  The  followers  of  the 
atomistic  school  believe  natural  phenomena  to  result 
from  the  impact  of  atoms,  possessing  mass,  figure  or 
extent,  indestructibility,  and  the  inherent  property  of 
motion.  Thus  this  idea,  adopted  by  Huygens,  agrees 
in  the  main  with  that  of  Newton,  except  as  it  rejects 
his  hypothesis  of  the  occult  power  of  attraction  of 
atom  for  atom  through  space.  With  Descartes  matter, 
as  a  distinct  and  separate  entity,  disappears  altogether, 
and  nothing  is  left  but  space  and  its  variations.  What 
we  call  pure  space  or  a  vacuum  is  really  a  continuous 
fluid  plenum  or  ether,  and  material  bodies  are  merely 
places  of  permanent  variation  in  this  plenum.  From 
observing  the  persistence  of  whirlpools  in  water  and  in 
the  air,  Descartes  ingeniously  concluded  that  all  space 
was  filled  with  whirlpools  or  vortices  of  this  plenum, 
each  having  an  axis  which  passes  through  one  of  the 
stars.  Unfortunately  for  the  theory,  these  vortices  and 
material  variations  of  space  soon  became  so  compli- 


TENDENCIES  OF  MODERN  PHYSICS      41 

cated  as  to  destroy  its  value.  In  the  last  century  the 
idea  was  revived  by  Lord  Kelvin  in  his  celebrated 
vortical  theory  of  matter.  He  used  only  the  main  ideas 
of  Descartes,  and,  from  a  better  mathematical  knowl- 
edge of  the  properties  of  vortices,  was  able  to  sim- 
plify their  character  and  to  account  for  many  of  the 
attributes  of  matter.  We  may  then  say  that  the  dis- 
similarity in  the  two  theories  consists  in  the  doctrine 
that  empty  space  is  a  vacuum  or  an  imaginary  entity 
called  the  ether,  as  opposed  to  the  postulate  of  Des- 
cartes that  space  is  true  material  substance ;  while  both 
theories  suppose  that  the  smallest  particles  of  sensible 
matter  are  indivisible,  the  atomistic  school  considers 
them  to  be  atoms,  inherently  indivisible  and  essen- 
tially different  from  space,  but  Descartes  declared 
them  to  be  variations  of  a  substance,  itself  infinitely 
divisible,  although  they  might  not  be  further  divisible 
by  our  present  experimental  ability.  With  this  under- 
standing of  Descartes's  hypothesis,  we  are  in  a  posi- 
tion to  show  how  closely  modern  views  of  matter  and 
electricity  are  concurring  in  this  idea. 

From  the  large  number  of  physicists  now  writing  on 
the  theory  of  physics,  three  names  stand  out  promi- 
nently as  originators  of  the  modern  conceptions  of 
electricity  and  matter.  Professor  H.  A.  Lorentz,  Sir 
Joseph  Larmor,  and  Sir  Joseph  Thomson  are  certainly 
the  men  who  will  be  most  prominently  associated  with 
this  movement;  others  have  aided,  but  mainly  in  the  ex- 


42          THE  LIMITATIONS  OF  SCIENCE 

tension  or  modification  of  their  ideas.  And  of  the 
three,  the  most  attention  in  an  essay  of  this  character, 
which  attempts  a  general  discussion  of  the  philosophical 
basis  of  scientific  theory,  should  be  devoted  to  Pro- 
fessor Larmor's  ideas.  In  his  treatise,  lEther  and 
Matter,  published  in  1900,  we  have  the  rather  rare 
example  of  a  scientific  theory  with  a  philosophical  back- 
ground clearly  expressed  and  discussed. 

The  main  thesis  of  his  essay  is  that  a  purely  me- 
chanical theory  of  discrete  atoms  moving  in  empty 
space  has  failed  to  account  for  the  phenomena  of 
nature,  and  especially  for  the  recent  discoveries  made 
in  electricity.  We  may,  however,  by  altering  this  con- 
ception of  atoms,  by  separating  electricity  and  matter 
into  two  entities,  or  even  by  considering  matter  as  an 
attribute  of  electricity,  again  reconcile  fact  and  hypoth- 
esis. Since  Faraday's  time  the  drift  of  opinion  has 
been  in  the  direction  of  this  separation,  so  that  it  is 
merely  necessary  to  crystallize  it  into  a  definite  scien- 
tific postulate.  No  idea  of  finality  is  expressed  in 
Professor  Larmor's  theory,  since  he  thinks  it  should 
endure  only  so  long  as  it  agrees  with  facts  in  our 
possession;  on  the  other  hand,  he  considers  it  not  to 
be  effective  criticism  to  make  a  charge  of  incomplete- 
ness without  indicating  a  better  way,  as  an  hypoth- 
esis may  be  valuable  not  only  when  imperfect,  but  when 
quite  wrong,  providing  it  serves  as  a  useful  instru- 
ment for  the  progress  of  natural  philosophy.  As  an 


TENDENCIES  OF  MODERN  PHYSICS       43 

instance  of  this,  he  states  that  many  of  the  most  im- 
portant discoveries  in  light  were  made  when  the  er- 
roneous corpuscular  theory  was  still  in  vogue.  But 
does  it  necessarily  follow  that  the  theory  prompted 
the  discoveries  or  led  to  their  investigation  because 
they  happened  to  be  contemporaneous?  It  is  difficult 
to  believe  Bradley  would  have  failed  to  obtain  the 
relation  between  the  aberration  of  light  and  its  finite 
velocity  if  some  other  theory  had  been  popular.  Cer- 
tainly the  specific  attributes  assigned  to  light  corpuscles 
would  have  little  influence  in  promoting  such  discover- 
ies, since  it  was  the  habit  to  modify  these  without  much 
compunction  if  they  did  not  square  with  observation. 
And  we  are  supported  in  this  opinion  by  Professor 
Larmor  himself  when  he  says :  "  At  the  same  time  all 
that  is  known  (or  perhaps  need  to  be  known)  of  the 
ether  itself  may  be  formulated  as  a  scheme  of  differen- 
tial equations,  .  .  .  which  it  would  be  gratuitous  to 
further  explain  by  any  complications  of  structure"; 
and  again :  "  The  ultimate  inadequacy  of  a  method  of 
treating  material  media,  based  on  merely  empirical  or 
speculative  additions  to  the  ascertained  equations  of 
free  ether,  had  indeed  been  clearly  recognized  by  von 
Helmholtz." 

The  questions,  then,  to  be  borne  in  mind  while  dis- 
cussing these  modern  theories,  are  whether  they  involve 
speculative  additions  to  our  equations  and  explanations 
by  complicated  constructions,  and  whether  they  are 


44          THE  LIMITATIONS  OF  SCIENCE 

essential  to  the  progress  of  science.  I  shall  try  to  show 
that  they  are  characterized  by  the  same  occult  and 
unverifiable  assumptions  as  the  older  theories  and  are 
really  extra-scientific. 

Professor  Larmor,  in  the  beginning  of  his  essay, 
recognizes  that  an  hypothesis  which  supposes  matter 
to  be  constituted  of  an  immense  number  of  discrete 
particles  moving  in  empty  space  and  incapable  of  fur- 
ther subdivision  has  a  philosophical  objection  too  diffi- 
cult to  be  overcome.  In  the  first  place,  as  Lord  Kelvin 
pointed  out,  the  chemical  atom  cannot  be  the  immeasur- 
ably small  body  sometimes  claimed  by  metaphysicians. 
Both  physical  and  chemical  experience  require  the  atom 
to  be  a  real  portion  of  matter  occupying  a  finite  space, 
and  forming  a  not  inappreciably  small  constituent  of 
any  palpable  body.  The  chemical  molecule  may  be 
decomposed  into  the  atoms  of  hydrogen  and  oxygen, 
and  now  these  atoms  are  in  turn  divided  into  sub- 
atoms.  Even  these  also  are  by  no  means  immeasurably 
small;  we  are  already  calculating  their  size  and  their 
mass.  And  we  can  think  of  no  reason  why  matter 
should  have  been  created  of  this  size  rather  than  any 
other.  These  minute  grains  still  have  much  individual- 
ity of  their  own  in  the  way  of  attributes;  if  electrified, 
their  mass  is  supposed  to  change  in  quantity  when  they 
move,  as  does  also  their  shape;  they  must  explain 
electrical  attraction  and  repulsion,  gravitational  at- 
traction, cohesion,  and  a  probable  molecular  repulsion 


TENDENCIES  OF  MODERN  PHYSICS      45 

known  as  elasticity ;  they  must  have  a  propensity  which 
makes  them  build  geometrical  crystals:  in  fact  they 
must  be  arbitrarily  and  occultly  endowed  with  all  the 
attributes  of  ponderable  matter  which  they  were  created 
to  explain.  This  sub-atom  has  many  more  duties  to 
perform,  but  sufficient  have  been  given  to  show  that 
either  it  is  excessively  complex  in  essence  or  is  en- 
dowed with  complex  forces;  so  far,  this  is  our  arbitrary 
resting  point  in  the  matter  of  subdivision,  but  it  is 
merely  a  temporary  makeshift.  But  there  is  a  still 
more  cogent  reason  for  this  philosophical  objection 
than  the  empirical  ones  given.  The  equally  funda- 
mental concepts  of  space  and  time  are  invariably  con- 
sidered as  continuous  or  infinitely  divisible  functions, 
and  this  theoretical  difference  assigned  to  matter,  in- 
troduces inevitable  trouble  in  mathematical  analysis. 
The  science  of  mechanics,  in  its  theoretical  aspect,  may 
be  defined  as  the  attempt  to  apply  the  laws  of  geometry 
to  real  bodies,  and  while  there  is  always  an  insurmount- 
able break  in  thought  between  the  laws  of  the  imag- 
inary bodies  discussed  in  geometry  and  the  concrete 
ones  of  mechanics,  we  can,  by  the  assumption  of  the 
continuity  and  indefinite  divisibility  of  matter,  approxi- 
mate as  closely  as  we  wish  to  the  rigorous  laws  of 
geometry.  The  geometrical  point  and  line  are  re- 
spectively abstract  bodies  of  no,  and  of  one,  dimension ; 
in  experimental  mechanics,  they  are  both  real  bodies  of 
three  dimensions, — the  point  is  the  atom  and  the  line 


46          THE  LIMITATIONS  OF  SCIENCE 

a  succession  of  them.  Theoretical  mechanics  is  thus 
the  link  between  geometry  and  physics,  for  while  it 
deals  with  concrete  bodies  of  real  size,  we  eliminate 
by  the  abstractive  method  all  the  variations  which  re- 
sult from  the  finite  size  of  bodies  and  then  discuss  them 
as  if  they  were  theoretically  simple  bodies  of  no  size. 
That  is,  we  divide  a  body  into  infinitesimal  portions 
and  consider  its  effect  as  being  due  to  the  arithmetical 
sum  of  the  effects  of  these  parts.  An  example  will 
make  this  clearer;  the  attraction  between  two  spheres, 
which  is  one  of  the  fundamental  problems  of  physics, 
can  be  solved  rigorously  only  by  the  application  of  the 
principle  of  centers  of  inertia,  that  the  attractive  force 
of  a  sphere  is  the  same  as  if  its  entire  mass  were  con- 
centrated at  its  mathematical  center.  As  soon  as  we 
apply  this  law  of  attraction  to  real  spheres,  even  of 
sub-atomic  size,  we  introduce  an  appreciable  error, 
since  the  attractive  force  then  produces  strains  and  a 
deformation  of  shape  which  reacts  to  change  the  force ; 
this  error  becomes  negligible  only  when  we  consider 
matter  to  be  continuous  and  the  sphere  to  be  made  up 
of  an  indefinitely  large  number  of  indefinitely  small 
particles.  We  are  thus  brought  to  this  dilemma;  ex- 
perimentally, matter  is  discontinuous  and  theoretically, 
it  is  continuous, — hypothesis  might  be  called  the  hope- 
less effort  to  reconcile  these  irreconcilables. 

Professor  Larmor  tries  to  avoid  this  pitfall,  which 
has  caught  the  originators  of  atomic  theories,  and  at- 


TENDENCIES  OF  MODERN  PHYSICS      47 

tempts  to  reconcile  the  antagonistic  ideas  of  continuity 
and  atomicity  by  placing  himself  squarely  on  the  side 
of  Descartes.  He  does  not  regard  space  as  mere 
empty  geometrical  continuity.  According  to  his  no- 
tion, the  universe  is  a  plenum  or  ether — that  is,  a  con- 
tinuous, frictionless  fluid,  everywhere  uniform  and 
quiescent.  This  plenum  constitutes  what  he  calls  trite 
matter.  It  is  entirely  unrecognizable  by  our  senses 
and  cannot  be  brought  to  them  by  any  experience.  By 
such  a  metaphysical  hypothesis  we  may  account  for 
the  aberration  of  light  and  many  other  actions  occur- 
ring in  free  space.  To  provide  for  ordinary  or  sensible 
matter,  making  it  at  the  same  time  discontinuous  in 
character,  he  supposes  there  exist  in  the  plenum  in- 
numerable places  of  variation,  which  are  uncreatable, 
indestructible,  and  humanly  indivisible,  and  by  their 
combination  present  to  our  senses  all  the  phenomena 
making  up  for  us  the  material  universe.  These  dis- 
continuities are  free  to  move  without  disturbing  the 
quiescence  of  the  continuous  medium,  much  as  wind 
blows  through  a  forest.  By  this  supposition  we  ac- 
count for  the  experimental  fact  that  motion  of  matter 
does  not  affect  the  velocity  of  light  in  a  vacuum.  If, 
however,  the  discontinuities  show  unbalanced  electrical 
force,  then  their  motion  causes  real,  although  tempo- 
rary, variations  in  the  medium. 

The  next  requirement  in  his  cosmogony  is  to  specify 
what  these  variations  in  the  supposititious  plenum  may 


48          THE  LIMITATIONS  OF  SCIENCE 

be.  This  is  the  vital  step  in  any  process  of  reasoning 
which  attempts  to  link  metaphysical  assumption  to 
physical  experience.  Once  taken  without  challenge,  a 
scientific  theory  may  be  developed  logically.  It  is  just 
at  this  point  that  the  Lucretian  atom  and  the  Cartesian 
vortex  fail.  Here  also  Lord  Kelvin  failed.  He  proved 
that  no  finite  force  could  either  create  his  tiny  vortex 
atom  rotating  in  a  f  rictionless  medium,  or,  once  started, 
could  stop  it.  He  showed  it  would  act  as  if  possessed 
of  many  of  the  essential  properties  of  matter.  But,  in 
the  process  of  elaboration,  this  atom,  like  all  others, 
became  unmanageable  from  complexity;  it  failed  to 
account  for  the  electric  charges  of  matter,  and  finally 
received  a  death-blow  when  Maxwell  said  a  vortex 
ring  might  be  an  analogy  to  the  atom,  but  at  best  was 
merely  a  mode  of  motion  and  not  matter  as  we  know  it. 
How,  then,  is  this  new  protoplasmic  element  of  the 
universe  to  be  defined  so  as  to  satisfy  these  criticisms, 
and  at  the  same  time  avoid  making  the  speculative  me- 
chanical structures  in  an  ether,  which  Professor  Lar- 
mor  deprecates?  The  founders  of  the  new  electrical 
theory  of  matter  have  studied  profoundly  the  laws  of 
nature.  They  have  made  many  permanent  acquisitions 
to  our  knowledge;  they  have  elaborated  their  theory 
with  the  greatest  ingenuity,  and  yet  the  result  has  been 
to  show  that  their  theory  is  merely  the  same  as  the  dis- 
carded ones,  amplified  and  clothed  in  new  names.  The 
additional  complexity,  due  to  the  desire  to  be  more 


TENDENCIES  OF  MODERN  PHYSICS       49 

exact  and  more  comprehensive,  will  do  more  than  the 
criticisms  of  its  adversaries  to  hasten  the  time  when 
physicists  will  frankly  avoid  metaphysical  explana- 
tions and  start  from  experimental  axioms. 

In  order  to  be  exact  when  defining  this  new  idea  of 
the  atom,  I  shall  quote  again  from  lEther  and  Matter: 
"  The  protion  (or  sub-atom)  must  therefore  be  in  whole 
or  in  part  a  nucleus  of  intrinsic  strain  in  the  ether,  a 
place  at  which  the  continuity  of  the  medium  has  been 
broken  and  cemented  together  again  (to  use  a  crude 
but  effective  image)  without  accurately  fitting  the 
parts,  so  that  there  is  a  residual  strain  all  round  the 
place."  So  far  this  might  almost  be  interpreted  as 
the  specification  for  a  vortex  atom;  but,  since  such  a 
type  of  strain  fails  to  provide  matter  with  electric 
charges,  he  diverges  at  this  point  and  considers  the 
"  ultimate  element  of  matter  to  be  an  electric  charge 
or  nucleus  of  permanent  ethereal  strain  instead  of  a 
vortex  ring." 

When  discussing  these  definitions,  we  should  bear 
constantly  in  mind  that  the  chief,  if  not  the  only,  pur- 
pose of  an  atomic  theory  or  of  a  mechanical  model  is 
to  create  a  picture,  however  crude,  of  the  constitution 
of  matter.  I  can  form  absolutely  no  mental  image  of 
such  a  kind  of  matter  as  Professor  Larmor  proposes, 
and  although  I  have  discussed  this  new  theory  many 
times  with  its  supporters,  I  have  never  found  them  able 
to  give  any  clear  and  simple  idea  of  such  a  strain;  it 


50          THE  LIMITATIONS  OF  SCIENCE 

is  certainly  unlike  any  that  we  have  encountered  in  ex- 
perimental mechanics  or  electricity.  Let  us  strip  the 
definition  of  technical  intricacies,  of  such  words  as 
protions  and  ethereal  electric  strains,  which  have  the 
power  of  confusing  the  mind  and  of  making  us  accept 
statements  we  do  not  quite  understand.  In  the  first 
place,  Professor  Larmor's  hypothesis  is  merely  an 
evasion  of  the  old  atomic  theory.  His  continuous,  true 
matter  which  has  absolutely  no  mechanical  attributes 
and  indeed  none  of  any  sort,  except  what  he  calls  the 
ability  to  be  modified  by  an  electric  charge,  seems  to 
me,  as  a  substance,  but  very  little  removed  from  my 
idea  of  mere  extent  or  abstract  geometrical  space. 
Sensible  matter  which  consists  of  discontinuous  varia- 
tions of  this  true  matter,  not  of  a  mechanical  nature 
but  of  what  he  calls  electrical  strains,  is  to  me  less 
substantial  than  extent  or  space;  for,  as  difficult  as  it 
may  be,  I  can  form  some  idea  of  space  and  I  can  com- 
municate this  idea  to  others,  but  I  can  make  no  mental 
picture  of  an  electrical  strain  in  a  non-mechanical 
plenum;  and  such  a  strain  certainly  does  not  impress 
me  as  being  matter  as  I  know  it.  I  shall  now  form 
these  ideas  into  a  chain :  space  is  substance ;  matter  is 
a  variation  or  strain  in  substance;  a  strain  is  an  elec- 
tric charge ;  an  electric  charge  is  matter ;  matter  is  sub- 
stance; therefore  an  electric  charge  and  matter  are 
both  space,  unless  I  can  be  persuaded  that  a  variation  of 
an  entity  can  change  its  essence,  which  is  absurd.  This 


TENDENCIES  OF  MODERN  PHYSICS       51 

is  a  rather  complicated  syllogism,  so  it  is  better  to 
reduce  it  to  simpler  terms,  as  follows :  true  matter  is  a 
plenum;  by  definition,  a  plenum  is  that  which  is  full  of 
matter ;  therefore  matter  is  true  matter.  Such  reason- 
ing should  convince  anyone  that,  no  matter  how  we 
may  wrap  up  our  logic,  we  cannot  explain  those  things 
which  we  must  use  as  a  means  of  explaining  other 
phenomena.  The  ordinary  man  expresses  this  by  the 
saying,  we  cannot  lift  ourselves  by  our  own  bootstraps. 
Are  not  such  hypotheses  in  the  same  class  as  perpetual 
motion  and  squaring  the  circle? 

But  even  on  the  scientific  side,  this  hypothesis  is  not 
satisfactory.  Every  theorist  acknowledges  that  sci- 
ence is  founded  ultimately  on  our  sense  perceptions, 
and  this  fact  should  warn  us  that  the  attribute  elec- 
tricity is  not  a  substance.  The  phrase,  to  electrify 
matter,  has  a  well-defined  meaning,  because  we  know, 
by  experience,  that  a  body  when  rubbed  exhibits  a 
force  which  was  not  evident  previously.  We  also  know 
that  we  may  select  two  different  bodies,  which  will 
each  show  this  electric  force  but  of  such  opposite 
characteristics  that  their  mere  contact  reduces  the 
whole  force  to  zero.  Our  knowledge  of  electricity 
comes  only  by  this  manifestation  of  electric  force,  so 
that  if  electricity  were  a  substance  we  are  reduced  to 
this  anomaly,  that  the  addition  of  substance  to  sub- 
stance may  result  in  less  substance.  This  attractive 
force  is  the  simple  and  fundamental  fact  in  regard  to 


52          THE  LIMITATIONS  OF  SCIENCE 

electricity  and  it  is  not  proper  to  avoid  it  by  speculating 
on  matter  in  a  state  so  special  and  so  removed  from 
common  experience  as  when  it  is  radio-active  or  highly 
vacuous.  Now  experience  teaches  us  that  matter  added 
to  matter  is  always  more  matter;  thus  satisfying  our 
prime  requisite  for  substance.  This  difference  between 
electricity  and  matter  is  sufficient  to  explain  why  the 
term  electrified  matter  is  a  real  idea,  and  why  material- 
ized electricity  means  nothing.  There  is  no  more 
justification  for  calling  electricity  a  substance  than  there 
is  for  doing  the  same  thing  for  any  other  attribute  of 
matter,  such  as  color  or  temperature.  The  simple  fact 
that  matter  appeals  directly  to  our  sense  organs  and 
electricity  does  not  should  be  sufficient  to  convince  any- 
one that  our  interpretation  of  nature,  because  of  our 
material  and  mental  organization,  must  be  based  for 
all  time  on  a  foundation  of  material  substance  and 
not  of  electrical  substance.  The  postulate  of  the  ob- 
jective existence  of  matter  is  a  necessary  hypothesis 
and  that  of  electricity  is  not.  Is  it  to  be  supposed  that, 
because  certain  learned  men  find  difficulty  in  explaining 
some  of  the  obscure  actions  of  matter,  the  human  race 
is  to  cast  aside  an  instinctive  and  universally  accepted 
axiom,  any  more  readily  than  it  will  discard  the  idea 
that  the  straight  line  is  the  shortest  distance  between 
two  points ;  that  parallel  lines  never  intersect ;  or  that  all 
bodies  require  three,  and  only  three,  dimensions  in 
order  to  locate  them; — because  a  few  modern  ge- 


TENDENCIES  OF  MODERN  PHYSICS       53 

ometers  choose  to  advance  other  and   contradictory 
postulates  as  axioms? 

Let  us  now  turn  to  some  of  the  specific  difficulties 
of  this  new  theory.  In  addition  to  many  absurd  prop- 
erties ascribed  to  the  old  elastic  solid  ether,  its  chief 
defects  were,  that  it  must,  at  the  same  time,  have 
friction  and  not  have  friction,  and  that  it  could  not 
account  for  electricity.  If  it  had  friction,  then  the 
ether  would  absorb  light  and  heat  energy,  and  the  mo- 
tion of  bodies  through  it  would  affect  the  properties  of 
light  in  a  manner  which  could  be  detected;  both  of 
these  have  been  found  to  be  contrary  to  experience. 
On  the  other  hand,  the  ether  must  have  friction  to 
permit  the  communication  of  atomic  vibrations  to  it. 
To  escape  these  dilemmas,  Professor  Larmor  supposes 
the  electro-magnetic  ether  to  be  without  mechanical 
friction  and  so  to  remain  quiescent  when  any  body 
moves  through  it,  but  he  apparently  forgot  that  he  had 
assumed  that  the  essence  of  substance  is  electricity. 
If  bodies  are  forms  of  electricity  how  can  they  move 
through  an  electrical  medium  without  disturbing  it? 
Since  we  have  abandoned  the  theory  that  light  and 
heat  are  mechanical  waves  for  the  supposition  that  they 
are  electro-magnetic  disturbances  caused  by  periodic 
variations  of  electric  charges,  the  new  ether  must,  in 
some  way,  be  modified  by  electric  variations  in  order 
to  receive  and  to  transmit  light  and  heat.  But  anyone 
can  see  we  are  just  where  we  started.  The  electro- 


54          THE  LIMITATIONS  OF  SCIENCE 

magnetic  ether  must  have  electro-magnetic  friction,  to 
receive  the  electro-magnetic  vibrations  of  the  electric 
atom  and  must  be  devoid  of  electro-magnetic  friction 
so  as  not  to  absorb  electro-magnetic  waves  when  in 
transit.  Again,  he  says  the  mechanical  atom  was  de- 
fective, in  that  it  could  not  account  for  electricity,  but 
he  also  says  that  the  electrical  atom  does  not  explain 
cohesion,  weight,  and,  I  might  add,  any  other  me- 
chanical property.  Which  shall  we  choose?  Lastly, 
not  to  prolong  the  discussion,  just  as  the  mechanical 
ether  and  atom  led  us  to  such  contradictory  attributes 
as  enormous  rigidity  and  inappreciable  density,  so  the 
electro-magnetic  ether  and  atom  require  us  to  give  the 
latter  an  electric  force  whose  magnitude  is  to  that  of 
weight  as  ten  raised  to  the  forty-second  power  is  to 
one. 

Temperamentally,  Professor  Thomson  has  little  in 
common  with  his  colleague,  Professor  Larmor;  as  all 
know,  we  owe  to  him  a  long  series  of  most  delicate  and 
profound  experimental  investigations  in  this  field. 
Like  Lord  Kelvin,  he  is  usually  content  to  construct  a 
model  for  each  special  phenomenon,  and,  as  he  is  rather 
indifferent  whether  these  agree  in  operation,  it  is  diffi- 
cult to  form  any  consistent  idea  of  his  theory.  He 
seems  to  regard  matter  as  if  it  were  a  sort  of  building- 
blocks  which  may  be  put  together  as  fancy  directs.  His 
best-known  conception  of  matter  and  electricity  is  his 
picture  of  an  atom  as  a  central  sphere  of  uniformly 


TENDENCIES  OF  MODERN  PHYSICS       55 

distributed  positive  electricity  with  points  of  negative 
electricity  so  placed  in  it  as  to  form  the  corners  of 
regular  geometrical  figures.  He  then  calculates  the 
stability  of  each  figure  from  the  mutual  attractions  and 
repulsions  of  the  charges  and  supposes  the  chemical 
elements  to  be  conditioned  by  this  stability.  The 
scheme  is  so  frankly  artificial  and  speculative  that  its 
author  can  regard  it  only  as  an  architect  does  his 
sketch,  as  a  symbol  of  a  house.  But  in  addition  to  his 
pictorial  representations  of  matter  and  phenomena, 
which,  if  taken  correctly,  do  not  deceive  anyone,  he 
subscribes  to  the  hypothetical  method  and  is  a  leader 
in  developing  the  electrical  theory  of  matter. 

If  we  now  turn  to  a  consideration  of  the  ideas  of 
Professor  Lorentz,  we  shall  find  a  close  agreement  with 
the  hypothesis  of  Professor  Larmor.  We  have  been 
led  to  the  conception  of  electrons  or  protions,  Professor 
Lorentz  says  in  his  Theory  of  Electrons,  by  our  de- 
sire to  understand  the  electrical  properties  of  matter. 
For,  while  we  adopt  the  theory  of  Faraday  and  Max- 
well that  the  space  or  electro-magnetic  ether  near  an 
electrically  charged  body  is  put  in  a  certain  state  of 
strain  and  never  lose  sight  of  this  idea,  yet  we  need 
not  form  an  image  of  it  and  really  cannot  say  much 
about  it.  In  fact,  these  strains,  as  imagined  by  them, 
cannot  have  a  real  existence  without  producing  motion 
in  the  ether,  which  is  an  impossible  assumption.  On 
account  of  the  difficulties  into  which  such  speculations 


56          THE  LIMITATIONS  OF  SCIENCE 

lead  us,  there  has  been  a  tendency  of  late  years  to  avoid 
them  altogether.  But  while  this  method  is  the  safer  one 
and  provides  us  with  a  set  of  correct  formulae  and  laws, 
yet  we  are  compelled  to  introduce  into  these  equations 
unknown  terms,  called  coefficients,  which  express  the 
individual  properties  of  different  kinds  of  ponderable 
bodies.  For  example,  the  same  magnetic  force  pro- 
duces different  magnetic  effects  in  iron  and  copper.  If 
we  wish  to  obtain  a  deeper  insight  into  the  properties  of 
matter,  he  says,  we  must  not  be  satisfied  with  simply 
introducing  for  each  substance  its  special  coefficient, 
whose  value  is  to  be  determined  by  experiment;  we 
must  invent  some  hypothesis  about  the  mechanism  of 
matter  which  causes  such  differences  of  behavior.  It 
is  this  necessity  which  has  led  us  to  the  hypothesis  of 
the  electron.  He  then  defines  these  electrons  as  ex- 
tremely small  particles,  charged  with  electricity,  and 
present  in  immense  numbers  in  all  ponderable  bodies. 
They  are  of  two  kinds,  positive  and  negative,  and  are 
free  to  move  in  conductors  of  electricity  and  bound 
to  points  of  equilibrium  in  non-conductors.  Sometimes 
he  considers  them  to  be  rigid,  and  at  other  times  as 
deformable  bodies.  Their  inertia,  or  mass,  is,  for  the 
most  part,  an  effect  of  their  electric  charge,  and  the 
negative  electron  is  probably  free  electricity  without 
ponderable  mass.  Professor  Lorentz  assigns  no 
specific  properties  to  the  ether,  but  he  is  required  to 
assume  that  it  can  penetrate  freely  all  parts  of  the 


TENDENCIES  OF  MODERN  PHYSICS       57 

electron.  It  is  evident  that  the  philosophical  ideas  of 
this  theory  are  the  same  as  those  previously  discussed. 
We  are  driven  in  both  to  the  supposition  that  the  elec- 
tron is  a  space  modification  of  a  universal  medium  and 
that,  in  some  way,  neither  electron  nor  ether  is  a  ma- 
terial substance,  but  a  kind  of  transcendental  entity 
called  electricity. 

Of  course  we  wish  to  obtain  a  deeper  insight  into  the 
properties  of  matter,  and  if  we  had  discovered,  or  had 
any  means  of  discovering,  a  method  to  such  a  knowl- 
edge, no  amount  of  labor  would  be  superfluous  while 
making  an  hypothesis.  But  we  wish  many  impossible 
things;  we  should  like  to  be  satisfied  about  the  im- 
mortality of  the  soul ;  the  causes  and  nature  of  life,  and 
a  host  of  other  problems.  Now  Professor  Lorentz 
says  we  know  very  little  about  the  ether  and  the  nature 
of  matter,  and  by  very  little,  he  means  we  know  noth- 
ing. What  advantage,  then,  does  he  propose,  when  he 
says:  Come,  let  us  invent  something  about  these  un- 
knowable things,  let  us  make  an  hypothesis  that  we 
may  seem  to  obtain  a  deeper  insight  into  the  mysteries 
of  nature?  He  knows  that  the  atom  of  iron  is  as  mys- 
terious as  a  ton  of  that  substance,  and  that  he  does 
nothing  to  explain  the  nature  of  iron  by  giving  imagi- 
nary properties  to  a  sub-atom  of  iron ;  he  is  aware  that 
he  has  not  touched  the  reason  why  iron  differs  from 
copper,  and  he  ought  to  know  that,  by  calling  this  sub- 
atom  a  particle  of  electricity,  he  has  only  added  con- 


58          THE  LIMITATIONS  OF  SCIENCE 

fusion  to  our  ignorance.  What  would  he  say  of  a 
biologist  who,  growing  tired  of  describing  forms  of 
life  which  he  can  handle,  gave  the  habits  and  appear- 
ance of  marine  animals  living  beyond  the  reach  of  his 
dredging  nets?  The  security  of  experimental  science 
rests  on  the  belief  that,  for  the  honor  of  science,  no 
one  will  tamper  with  what  he  has  actually  observed. 
Why  should  more  leniency  be  granted  the  theorist, 
why  should  he  be  allowed  to  mix  fact  and  fancy,  law 
and  hypothesis,  as  he  chooses,  and  not  be  called  to  ac- 
count? It  is  just  this  restraint,  this  distinguishing 
between  what  we  know  and  what  we  desire,  that  con- 
stitutes the  value  of  science  as  a  discipline  of  the  in- 
tellect; and  in  the  exercise  of  this  restraint  lies  our  in- 
tellectual integrity.  The  gospel  of  science,  for  it  has 
one  as  truly  as  has  religion,  may  be  summed  up  in  the 
words  of  Goethe :  "  in  restraint  first  shows  himself  the 
master.''  What  has  it  come  to,  when  we  can  pass  over 
such  false  methods  with  a  shrug?  Huxley  spent  his 
life,  in  season  and  out  of  season,  waging  battle  with 
bishops  and  laymen  to  convince  them  that  religious 
belief  and  religious  theory  must  square  with  objective 
fact.  And  he  assured  them  that  men  of  science  could 
provide  a  foundation  of  truth,  and  would  not  impose  a 
false  one,  so  that  all  men  might  know  and  have  a  ra- 
tional basis  of  life  and  belief.  And  how  have  we  kept 
the  faith?  We  have  given  with  equal  emphasis  our 
speculations  and  our  observations.  Nor  can  Professor 


TENDENCIES  OF  MODERN  PHYSICS       59 

Lorentz  say  he  has  kept  in  the  certain  path  because  he 
has  warned  us  in  the  beginning  of  his  treatise  that  he 
is  dealing  with  glittering  hypothesis.  He  takes  all  the 
force  out  of  the  warning  by  using  his  genius  to  overlay 
his  speculations  with  a  specious  appearance  of  reality. 
Let  him  try  the  opposite  plan  and  actually  convince  a 
class  of  students  and  educated  men  generally  that  his 
hypothesis  does  not,  and  cannot,  give  any  real  insight 
into  the  actual  properties  of  matter,  that  he  is  talking  in 
a  Pickwickian  sense,  and  how  much  serious  attention 
would  he  attract?  No,  the  world  still  believes  in  the 
restraint  of  men  of  science  and  in  their  boast  that  they 
will  submit  our  vague  longings  to  the  test  of  experi- 
ence. And  it  will  be  a  bad  day  for  science  if  this 
belief  is  destroyed. 

Nor  is  it  proper  to  adopt  an  attitude  of  indifference 
to  these  hypotheses  as  many  experimentalists  do,  to 
pass  them  by  with  a  shrug  or  with  the  statement  that 
they  cause  little  harm  to  the  growth  of  science,  how- 
ever little  they  may  aid  it.  If  science  were  merely  a 
mental  gymnastics,  this  indifference  would  be  well 
enough,  but  science  is  increasingly  considered  to  be  a 
guide  to  conduct.  We  have  no  right  to  approve  the 
intellectual  carelessness  which  has  been  so  vividly  ex- 
pressed by  M.  Poincare  in  the  preface  to  his  The  one 
de  la  Lumiere:  "  It  matters  little  to  us  whether  the 
ether  really  exists;  that  is  the  business  of  the  meta- 
physician to  find  out;  the  essential  thing  for  us  is  that 


60          THE  LIMITATIONS  OF  SCIENCE 

everything  acts  as  if  it  existed  [?]  and  that  this 
hypothesis  is  convenient  in  explaining  phenomena. 
After  all,  have  we  any  other  reason  for  believing  in  the 
existence  of  material  objects?  Is  not  that  belief  also 
a  convenient  hypothesis;  only  we  shall  never  cease  to 
make  it,  meanwhile  the  time  will  come,  without  doubt, 
when  the  ether  will  be  rejected  as  useless."  Both  ma- 
terial objects  and  the  ether  may  be  only  hypotheses,  or 
rather  our  knowledge  of  them  is  relative,  but  not  in 
the  same  way;  the  existence  of  material  objects  is 
based  on  direct  experience  and  the  existence  of  the 
ether  is  not.  However  we  may  argue,  the  objective 
reality  of  matter  is  a  necessary  idea,  fixed  in  our  minds 
and  not  to  be  dislodged. 

Criticism  is  now  often  directed  against  the  older 
atomic  theory  because  a  given  form  of  it  no  longer 
accords  with  phenomena  which  have  been  lately  dis- 
covered. And  it  should  be  borne  in  mind  that  this  new 
theory  of  electrons  has  been  developed  with  the  main 
purpose  of  supporting  the  atomic  theory  and  making  it 
agree  with  our  new  knowledge  of  electricity.  Thus 
Professor  Rutherford  has  recently  performed  a  beau- 
tiful experiment  by  which  he  detects  electrically  a  por- 
tion of  helium  gas,  which  he  calculates  to  be  of  the 
dimensions  of  a  chemical  atom.  Here,  he  says,  we 
have  at  last  an  actual  experimental  proof  of  the  reality 
of  the  chemical  atom.  Does  not  this  experiment  show 
just  the  reverse?  The  idea  underlying  all  atomic 


TENDENCIES  OF  MODERN  PHYSICS       61 

theories  is  that  the  indivisible  unit  of  matter  is  so  small 
that  it  can  be  dealt  with  experimentally  and  mathe- 
matically in  aggregates  only.  So  when  he  devises  an 
apparatus  so  delicate  as  to  detect  the  action  of  a  single 
particle  the  size  of  the  so-called  chemical  atom,  he 
forces  us  to  adopt  for  the  real  atom  a  smaller  unit 
whose  individual  variations  will  be  beneath  our  obser- 
vation. The  unit  of  matter  becomes  just  one  degree 
further  removed  from  matter  as  we  know  it.  Instead 
of  squaring  our  hypotheses  with  the  sensible  proper- 
ties of  matter,  we  may  thus  more  easily  make  matter  a 
purely  transcendental  quantity  which  we  create  ac- 
cording to  our  own  imaginations.  Would  it  not  be  bet- 
ter frankly  to  say  the  material  universe  is  merely  a 
world  of  ideas,  an  embodiment  of  intangible  motion, 
energy,  and  electricity,  rather  than  to  keep  up  the 
fiction  that  the  electron  is  the  ultimate  unit  of  sub- 
stance ? 

Apparently  the  chemical  molecule  is  a  well-defined 
point  in  the  regular  divisibility  of  matter  where  cer- 
tain physical  apparatus,  as  the  balance,  fail  to  record 
variations  in  so  small  a  body;  but,  by  the  use  of 
chemical  appliances,  we  are  able  to  take  note  of  still 
smaller  masses,  which  have  been  named  the  atoms  of 
the  chemical  molecules.  At  this  point  these  methods 
become  too  gross,  and  we  next  have  recourse  to  the 
electrification  of  the  gaseous  atoms  by  the  X-rays  or 
by  radium,  and  can  then  detect  variations  in  these 


62          THE  LIMITATIONS  OF  SCIENCE 

particles  by  means  of  the  electroscope.  These  smaller 
portions  of  matter  are  called  electrons  or  sub-atoms, 
and  for  the  time  being  we  have  rested  here.  But  would 
anyone  say  that  new  methods  of  analysis  and  new 
apparatus  of  registration  are  an  impossibility,  and 
that  the  electron  will  not  in  future  be  divided?  On 
the  other  side  of  the  series  the  mote,  dancing  in  the 
sunbeam  and  disappearing  when  the  light  fails  it,  is  an 
indivisible  atom  to  the  unskilled  man  deprived  of  sensi- 
tive apparatus.  The  fact  is,  the  atom  as  an  objective 
unit  of  matter  has  no  existence ;  we  name  that  portion 
of  matter  an  atom  when  we  have  reached  a  limit  of 
appreciation  of  matter  by  our  most  sensitive  apparatus. 
If  these  fundamental  and  irrational  assumptions  of 
plenum  and  sub-atom  be  once  granted,  then  a  me- 
chanical explanation  of  many  of  the  phenomena  of  na- 
ture follows  logically.  But  this  is  also  true  if  we 
postulate  that  matter  is  composed  of  the  four  es- 
sences,— earth,  air,  fire,  and  water;  and  one  has  only  to 
recall  the  success  of  Descartes  with  his  three  elements. 
The  question  is,  are  the  postulates  true?  If  we  can- 
not verify  them  by  experiment,  then  science  should 
reject  them.  On  this  criterion  the  sub-atom  is  as 
vulnerable  as  any  other  postulate.  The  conclusions, 
deduced,  may  give  a  truly  mechanical  explanation ;  for, 
in  spite  of  denying  the  existence  of  matter  in  the  be- 
ginning, the  substitute  electricity  is  at  once  endowed 
with  all  the  essential  characteristics  of  the  discarded 


TENDENCIES  OF  MODERN  PHYSICS       63 

matter,  such  as  inertia,  conservation,  gravitational  at- 
traction, extent,  etc.  Certain  additional  properties 
add  to  its  conquests,  since,  by  splitting  up  the  atoms,  a 
new  set  of  pawns  is  available  to  the  players  of  this 
game  of  probability  and  chance. 

The  diversity  of  the  chemical  elements  may  be  said 
to  result  from  the  various  stable  combinations  which 
the  sub-atoms  may  be  made  to  assume.  Professor 
Rutherford  developed  his  ingenious  theory  of  radio- 
activity by  supposing  certain  elements  to  be  in  a  state  of 
comparatively  unstable  equilibrium.  A  definite  pro- 
portion of  their  atoms  explodes  continuously,  reduc- 
ing the  atomic  weight  of  the  parent  body,  and  supply- 
ing the  spontaneous  energy  noted  experimentally.  This 
process  continues  until  a  stable  form  is  reached.  But 
does  he  not  forget  that  one  of  the  triumphs  of  the  old 
atomic  theory,  a  proof  that  the  chemical  atom  could 
never  be  divided  into  sub-atoms,  was  that  when  an  un- 
stable compound,  like  gunpowder,  exploded,  the  con- 
stituents were  found  to  be  stable  chemical  atoms? 

The  phenomena  of  electricity  are  naturally  the  main 
problems  attacked.  A  current  of  electricity  in  this  new 
hypothesis  becomes  the  flow  of  immaterial  particles 
of  electricity  in  a  metal  conduit,  carrying  with  them 
their  energy  of  motion.  In  non-conductors,  like  glass, 
they  may  be  heaped  up  into  an  excess  of  positive  or 
negative  to  provide  a  picture  of  the  free  charges  on  such 
substances.  Radiant  light,  heat,  and  electricity  are 


64          THE  LIMITATIONS  OF  SCIENCE 

the  periodic  disturbances  produced  in  the  plenum  by  the 
oscillatory  motions  of  the  same  particles  about  fixed 
centers.  These  are  said  to  be  useful  ideas  and  clear 
explanations.  But  are  they?  Have  we  accomplished 
anything  more  than  to  reaffirm  the  statement  that  a 
current  of  electricity  under  certain  conditions  flows 
through  a  wire,  when  we  say  a  stream  of  charged  par- 
ticles moves  through  the  wire?  In  the  first  place,  we 
create  the  particles,  and  next  endow  them  with  an 
occult  power  of  motion.  Again,  when  zinc  and  cop- 
per are  placed  in  contact  and  separated,  the  zinc  be- 
comes positively  charged  with  electricity,  the  copper 
with  negative,  and  the  two  attract  each  other.  Do  we 
learn  anything  more  when  we  affirm  that  an  excess  of 
positive  electrical  particles  passes  into  the  zinc  and 
negative  ones  into  the  copper  ?  Why  should  they  act  so  ? 
In  both  cases  we  have  merely  stated  an  unknowable 
cause  in  different  words.  The  law  remains  the  same 
whether  we  say  electricity  or  electrical  particle,  and 
the  former  term  expresses  less  pretense  of  knowledge. 
Far  more  significant,  and  less  justifiable  even,  is  the 
attempt  to  explain  the  mass  of  a  body  as  an  attribute  of 
electricity.  Mathematical  analysis  shows  that  an  elec- 
trically charged  body,  moving  with  great  velocity,  has 
a  resistance  to  motion  apparently  greater  than  when 
not  so  charged.  Now,  they  say,  continually  diminish 
the  ponderable  mass  of  the  body  and  maintain  the  elec- 
tric charge  constant ;  the  electro-magnetic  mass,  as  this 


TENDENCIES  OF  MODERN  PHYSICS       65 

effect  of  electricity  is  called,  becomes  proportionately 
greater  and  greater.  Continue  this  process  indefinitely, 
and  at  last  all  the  matter  is  gone,  and  there  remains  a 
free  electric  charge,  an  immaterial  point  of  electricity, 
moving  and  possessing  inertia  or  mass.  And  just  here 
lies  the  greatest  danger  of  all  such  hypothesis — a  total 
confusion  of  fact  and  fancy.  In  the  first  place,  it  is 
not  even  based  on  experience,  since  the  most  rapidly 
moving  bodies  of  a  sensible  size  have  a  velocity  far 
too  little  to  make  this  effect  noticeable.  But,  what 
is  more  important,  it  is  a  method  of  thought  to  be  used 
with  the  utmost  caution  even  in  experimental  processes. 
The  warning  against  such  extra-polation  is  metaphor- 
ically displayed  in  every  physical  laboratory.  How  we 
would  scorn  the  unscientific  conclusions  of  the  meta- 
physicist  who  reasoned  in  the  same  way!  Let  us 
imagine  one  saying  that  goodness  is  an  attribute  of 
small,  as  well  as  of  large  men;  now  diminish  the  size 
of  a  man  and  let  his  quality  of  goodness  remain  con- 
stant, then  we  shall  have  an  entity,  concrete  goodness, 
left  when  the  man  shrinks  to  nothing.  It  is  not  neces- 
sary to  use  such  an  absurd  example,  as  a  parallel  case 
exists  in  physical  phenomena.  A  sphere,  moving  in 
a  fluid,  experiences  a  like  increase  in  apparent  mass, 
due  to  the  necessity  of  imparting  energy  to  the  fluid. 
Now  decrease  continually  the  density  or  mass  of  the 
body  and  maintain  its  volume  and  velocity  constant; 
the  hydrodynamic  mass  becomes  proportionately 


66          THE  LIMITATIONS  OF  SCIENCE 

greater.  Continue  this  process  until  the  matter  is  all 
gone,  and  there  is  left  a  sphere  of  something  with  an 
apparent  mass  still  moving  through  the  fluid.  Will 
it  not  be  difficult  to  persuade  anyone  that  the  something 
moving  did  not  vanish  simultaneously  with  the  mar- 
terial  sphere — that  the  attribute  did  not  vanish  with 
the  entity?  It  will  be  just  as  hard  to  convince  the 
future  scientist,  when  the  vogue  of  the  electrical  theory 
departs,  that  an  electrical  charge  remains  after  the  elec- 
trified matter  is  reasoned  away.  Such  ideas  leave  us 
in  the  same  foolish  state  as  the  hunters  of  the  Snark, 
who,  after  incredible  labors,  came  to  the  place  where 
a  Snark  should  be,  and  found  it  was  a  Boojum  which 
vanished  silently  away. 

If  I  am  correct  in  believing  the  fallacy  to  lie  in  try- 
ing to  explain  natural  laws,  it  is  not  pertinent  to 
inquire  further  into  the  working  of  this  electrical 
hypothesis.  The  essential  point  is  whether  physics  has 
anything  to  do  with  the  nature  of  matter  and  elec- 
tricity. Atoms  and  ethers  of  any  kind  are  metaphys- 
ical creations;  the  mechanical  models  built  on  such  an 
unsubstantial  foundation  require  a  god  to  set  them  go- 
ing, and  are,  at  best,  an  ineffectual  means  of  describing 
phenomena  previously  observed,  and  not  finger-posts 
to  new  discoveries. 

The  claim,  that  such  arguments  as  this  are  ineffectual 
criticism  because  they  tend  to  destroy  the  scientific 
method  most  used  and  offer  nothing  better  in  its  stead. 


TENDENCIES  OF  MODERN  PHYSICS      67 

is  frequently  made  by  scientific  theorists  who  recognize 
the  artificiality  of  their  hypotheses  but  who  feel  that,  in 
some  way,  they  tend  to  good.  They  forget  that  the 
growth  of  science  has  always  been  largely  due  to  the 
discovery  and  the  elimination  of  error.  If  we  wish  to 
make  a  garden,  the  first  necessity  is  to  clear  away  the 
weeds,  and  the  same  is  true  of  science ;  it  is  as  impor- 
tant to  know  what  is  wrong  as  what  is  right.  But 
even  this  claim  is  not  correct,  the  better  method  is 
known  and  is  in  use.  Have  they  forgotten  the  work  of 
Galileo,  of  Newton,  of  Franklin,  and  of  many  others, 
who  employed  the  abstractive  method,  or,  at  least,  kept 
their  hypotheses  well  in  the  background?  Nor  is  it 
difficult,  if  one  studies  the  history  of  physics,  to  out- 
line the  basis  of  a  method  in  harmony  with  my  ideas, 
as  I  shall  do  in  a  later  chapter. 

Nothing  has  been  more  convincing  to  me  of  the 
advantages  of  the  abstractive  over  the  hypothetical 
method  than  a  study  of  Descartes's  Principia  Naturae. 
Modern  theorists  have  acknowledged  their  debt  to 
him ;  how  great  is  this  obligation  can  be  seen  from  the 
discussion  of  Descartes's  system  which  follows.  A 
comparison  of  his  postulates  and  conclusions  with 
those  of  our  modern  theory  shows  them  to  be  almost 
identical,  if  we  change  his  antiquated  knowledge  and 
his  discarded  metaphysical  language  into  modern 
terminology.  And  lastly  we  should  compare  Descartes 
with  modern  physicists ;  his  knowledge  of  the  phenom- 


68          THE  LIMITATIONS  OF  SCIENCE 

ena  and  laws  of  nature  is  insignificant,  so  great  has 
been  our  progress  in  this  respect,  but  as  a  metaphys- 
icist  he  is  still  the  master  of  modern  scientific  hypoth- 
esis, so  little  has  been  accomplished  in  that  field  in  two 
hundred  years. 


CHAPTER  III 

DESCARTES  AND  HIS  INFLUENCE  ON 
RECENT  SCIENCE 

De  s'6garer  avec  methode. — MICHELET. 

IF  it  be  true  that  the  permanent  advances  made  in 
science  have  been  the  result  of  observing  phenomena 
and  of  classifying  them  in  laws  which  are  as  often  as 
possible  to  be  expressed  by  mathematical  formulae ;  and 
if  it  be  also  true  that  we  have  persisted  in  the  effort 
to  explain  the  causes  of  phenomena  without  really 
advancing  knowledge;  then  it  will  be  most  useful  to 
compare  our  present  state  with  that  of  an  earlier  time. 
For  this  purpose,  I  have  chosen  to  sketch  the  scientific 
system  of  Descartes.  In  the  first  place,  there  can  be 
no  doubt  as  to  the  enormous  increase  in  our  positive 
knowledge  of  phenomena  and  natural  laws  since  his 
time;  the  difference  is  so  great  that  there  is  no  need 
to  dwell  on  it.  And  yet,  if  we  consider  the  history  of 
Descartes's  hypothetical  cosmogony,  we  learn  that  it 
was  discarded  only  to  have  a  revival  at  the  present 
time.  The  advantage  of  reviewing  the  system  of  Des- 
cartes is  all  the  greater  because  it  seems  apparent  that 
many  of  those  who  are  quoting  his  authority  have  not 
an  accurate  knowledge  of  what  he  taught. 

69 


70          THE  LIMITATIONS  OF  SCIENCE 

So  far  as  I  can  see  the  hypothetical  method  has  its 
most  illustrious  example  in  Descartes,  and  instead  of 
aiding  us  to  gain  real  and  clear  ideas,  he  has  burdened 
science  with  useless  and  complicated  metaphysical  sys- 
tems. Instead  of  being  a  symptom  of  power,  the  reluc- 
tance to  recognize  the  limits  of  science  comes  rather 
from  a  certain  intellectual  cowardice  which  refuses  to 
acknowledge  the  truth,  that  we  cannot  attain  any  knowl- 
edge of  things  themselves  but  only  of  their  attributes 
as  they  affect  our  senses.  If  we  really  face  the  ques- 
tion; strip  our  scientific  hypotheses  of  their  technical 
phraseology  and  complex  logic,  and  try  to  get  a  clear 
and  simple  idea  of  what  they  mean,  we  find  that  we 
have  been  deceiving  ourselves.  In  the  first  place,  we 
use  words,  which  ordinarily  convey  definite  ideas,  in  a 
sense  purely  symbolical,  and  then  confuse  the  image 
and  the  reality.  For  example,  when  we  define  space 
or  the  ether  as  a  perfect  fluid,  we  deceive  ourselves 
into  believing  that  we  have  gained  a  clearer  idea  of 
space  by  applying  to  it  a  term  which  signifies  the 
mobility  of  matter.  But  this  attribute  can  be  applied 
only  to  a  material  fluid  whose  change  of  position  may 
be  measured,  and  such  a  fluid  appeals  to  us  as  some- 
thing essentially  different  from  immaterial  space.  Nor 
do  we  overcome  this  difficulty  by  qualifying  space  as 
a  perfect  fluid;  any  fluid  is  perfect  which  satisfies  the 
laws  of  its  nature,  and  we  practice  deception  when  we 
inject  the  ethical  meaning  of  perfect,  as  being  some- 


INFLUENCE  ON  RECENT  SCIENCE        71 

thing  above  ordinary  criticism,  into  the  scientific 
definition  of  a  fluid.  We  have  also  constructed  a  sym- 
bolic language,  called  mathematical  analysis,  whose 
characters  and  terms  are  so  removed  from  ordinary 
speech  that  it  imposes  on  our  minds  an  impression  of 
not  being  limited  by  the  bounds  of  logic.  Thus,  if  we 
derive  a  mathematical  formula  for  the  quantity  of 
heat  or  electrical  energy  which  passes  through  free 
space,  we  deceive  ourselves  by  thinking  that  we  have 
an  expression  not  only  for  a  quantity  of  energy,  but 
that  also  we  have  in  some  unaccountable  way  gained 
a  knowledge  of  the  nature  of  energy  and  of  the  at- 
tributes of  space.  And  we  slur  over  the  scientific 
axiom,  that  since  these  mathematical  symbols  did  not 
express  in  the  beginning  something  concrete,  they  can- 
not after  any  manipulation  give  a  result  which  is  other 
than  imaginative.  Again,  we  postulate  some  entity 
such  as  matter,  energy,  or  electricity,  as  a  foundation 
and  attempt  to  derive  logically  from  it  all  the  phe- 
nomena of  nature,  and  ignore  the  plain  fact  that 
nature,  as  a  whole,  reveals  itself  to  us  as  a  succession 
of  events,  either  not  connected  at  all  in  a  logical  se- 
quence of  cause  and  effect,  or  at  least  in  such  an  intri- 
cate tangle  as  to  defy  our  powers  of  analysis. 

During  the  last  two  decades,  there  have  been  dis- 
covered an  unusually  large  number  of  physical  phe- 
nomena, and  it  is  no  exaggeration  to  say  that  we  have 
mastered  them  with  surprising  rapidity  and  with  great 


72          THE  LIMITATIONS  OF  SCIENCE 

ingenuity.  At  the  same  time  we  have  turned  to  these 
new  manifestations  of  matter  and  energy  with  the 
hope  that  in  them  we  have  at  last  found  the  materials 
for  a  new  and  lasting  scientific  cosmogony.  But  the 
edifice  differs  in  appearance  only  from  that  built 
long  ago  by  Descartes;  and  the  materials  in  both 
are  the  same,  changed  in  name  but  not  in  sub- 
stance. 

By  a  scientific  cosmogony,  as  distinguished  from 
revelation  and  from  metaphysics,  is  here  meant  that 
we  first  postulate  an  archetypal  form  of  substance  and 
certain  fundamental  forces,  few  in  number  and  in- 
herent in  this  entity,  and  that  then  the  universe,  as  it 
now  exists,  follows  as  the  result  of  the  continued 
action  of  these  forces  on  this  substance.  That  is,  the 
state  of  the  universe  may  be  expressed  at  any  time 
subsequent  to  the  initial  action  of  the  forces  by  a  set 
of  mathematical  or  verbal  formulae.  And  if  we  could 
actually,  as  we  can  theoretically,  reverse  the  action  of 
these  forces  in  time  and  in  direction,  the  primal 
condition  of  the  universe  would  again  result.  It  is 
furthermore  postulated  that  this  archetypal  substance 
existed  originally  in  the  form  of  minute  particles, 
separate  from  each  other  and  exactly  similar  in  char- 
acter, and  that  the  forces  acting  on  these  particles  were 
in  such  perfect  balance  that  the  total  value  of  their 
effect  was  zero.  From  some  cause,  generally  unex- 
plained, this  balance  was  destroyed  and,  like  a  clock 


INFLUENCE  ON  RECENT  SCIENCE        73 

when  its  pendulum  has  once  been  jogged,  the  panorama 
of  cosmical  history  unrolls  itself  inexorably.  Thus 
the  universe  becomes  a  sort  of  machine  whose  parts  are 
mechanically  driven,  not  by  some  external  motive  force, 
but  by  the  mutual  reactions  of  its  parts,  and  so  destined 
in  time  to  run  down  when  this  internal  and  available 
energy  shall  have  exhausted  itself.  And  when  we 
speak  of  the  universe,  all  that  part  of  it  designated 
as  living  bodies  and  vital  forces  is  to  be  included,  be- 
cause of  the  belief  that  they  also  can  be  considered  as 
ponderable  masses  subject  to  physical  and  chemical 
forces. 

As  an  original  hypothesis  the  work  of  Lucretius  is 
of  no  consequence.  In  fact  his  atomic  theory  was 
taken  almost  entirely  from  Democritus,  and  it  was 
rather  by  the  vision  of  the  poet  than  by  the  logical 
analysis  of  the  man  of  science  that  he  developed  these 
ideas  into  a  picture  of  the  nature  of  our  world.  His 
theory  was,  in  brief,  that  the  universe  contained  in  an 
otherwise  empty  space  an  indefinite  number  of  indivis- 
ible and  immeasurably  small  particles,  called  atoms, 
which  differed  only  in  size,  position,  and  shape.  These 
atoms  were  indestructible  and  by  their  combination 
and  separation  formed  all  natural  bodies.  The  motion 
of  the  atoms  did  not  arise  from  external  forces  but 
was  an  inherent  property  of  their  nature.  With  a  com- 
mon impulse,  they  all  moved  toward  the  center  of  the 
universe,  but  in  addition  they  possessed  an  individual 


74          THE  LIMITATIONS  OF  SCIENCE 

power  of  irregular  deflexion  which  introduced  variety 
in  matter.  By  their  union  they  formed  bodies;  and  by 
their  impact  and  rebound  they  caused  vortical  motions 
which  now  find  expression  in  our  term,  energy.  As  an 
explanation  of  natural  phenomena  the  theory  has  no 
value,  as  it  originated  long  before  the  mathematical 
laws  of  forces  had  been  formulated  or  the  phenomena 
of  matter  had  been  accurately  observed;  but  as  a  guide 
to  thought  it  has  been  the  basis  of  most  of  the  later 
scientific  theories.  Gradually  elaborated  by  Gassendi, 
Newton,  Boyle,  Kant,  Laplace,  Dalton,  and  others, 
this  atomic  theory  is  still  the  touchstone  of  modern 
chemistry  and  physics. 

Possibly  the  vastest  consequence  of  the  atomic 
theory  is  the  nebular  hypothesis  developed  independ- 
ently by  Kant  and  Laplace.  Essentially  this  theory 
is  a  restatement  of  the  ideas  of  Democritus  and  Lucre- 
tius, yet  the  discovery  by  Newton  of  the  mathematical 
law  of  the  force  of  gravitation  permitted  for  the  first 
time  a  true  scientific  method.  Thus,  while  they  were 
compelled  to  assume,  as  arbitrarily  as  did  Lucretius,  an 
initial  state  of  chaos  when  matter  was  scattered  in 
atomic  masses  throughout  space,  they  nevertheless  had 
a  cause  when  for  any  reason  the  original  balance  of 
forces  was  disturbed,  experimentally  verified  and 
mathematically  expressed,  to  account  for  the  gradual 
agglomeration  of  atoms  into  larger  masses  at  definite 
places,  from  the  fact  that  any  two  masses  of  sensible 


INFLUENCE  ON  RECENT  SCIENCE        75 

size  were  known  to  have  a  mutual  attraction  varying 
inversely  as  the  square  of  the  distance  between  their 
centers.  The  active  attribute  of  matter,  ruling  and 
guiding  its  motion,  thus  became  independent  of  fancy 
and  subject  to  experimental  verification.  The  nebular 
hypothesis  has  remained  more  or  less  a  fragment, 
limited  to  the  determination  of  the  sizes,  masses,  and 
positions  of  celestial  bodies  and  systems.  Neither  Kant 
nor  Laplace,  except  for  a  discussion  of  temperatures, 
included  in  their  scheme  of  the  evolution  of  inorganic 
matter  the  causes  of  the  complex  forms  and  forces 
of  matter  now  observed  on  the  earth  or  stars.  Nor 
beyond  assuming  that  matter  was  determined  by  mass 
and  an  inherent  power  of  attraction,  did  they  make  any 
attempt  to  explain  how  this  occult  force  acted  through 
a  distance.  And  from  this  simplified  idea  of  matter 
without  variety  and  without  complexity,  they  were 
able  to  deduce  mathematically  and  logically  the  idea  of 
the  evolution  of  cosmical  matter,  from  a  condition  of 
primitive  distribution,  at  least  to  its  segregation  into 
cosmical  systems:  suns,  planets,  and  satellites.  And 
if  we  remember  that  Kant  approached  the  problem 
from  the  standpoint  of  the  metaphysician  and  Laplace 
from  that  of  the  pure  mathematician,  we  can  readily 
understand  why  they  both  were  satisfied  to  take  such  an 
abstract  view  of  the  universe,  and  also  the  simplicity 
and  the  insufficiency  of  such  a  method.  Astronomy  is 
the  one  science,  because  of  the  comparatively  enormous 


76          THE  LIMITATIONS  OF  SCIENCE 

magnitude  of  its  units,  which  permits  such  an  abstract 
simplification  of  matter  as  to  consider  it  merely  in  the 
form  of  masses  concentrated  at  mathematical  points. 
Where  we  deal  with  bodies  measured  in  millions  of 
tons  and  with  distances  in  millions  of  miles,  such  varia- 
tions as  are  found  in  the  laboratory  sink  into  com- 
parative insignificance  and  we  can  deal  with  averages 
instead  of  particulars.  On  tEe  whole  their  attempt  was 
a  success  since  we  can  find  few  flaws  in  the  general 
conception  of  a  nebular  hypothesis,  however  we  may 
differ  as  to  details.  And  just  because  the  phenomena 
discussed  are  so  few  in  number  and  so  general  in  char- 
acter, there  was  not  the  need  for  supposititious  causes 
and  fictitious  attributes,  provided  we  grant  their  initial 
state  of  the  universe  and  the  first  cause  contributing  to 
irregularity  and  the  beginning  of  motion.  These  pos- 
tulates are  of  course  entirely  arbitrary  and  require 
us  to  assume  an  existence  previous  to  time,  since  time 
has  no  meaning  in  a  universe  which  is  everywhere  in  a 
state  of  perfect  equilibrium  and  rest.  Undoubtedly 
the  reason  why  this  hypothesis  persists  in  its  principal 
features  to  the  present  time,  in  spite  of  constant 
attacks,  is  just  because  its  authors  exercised  self- 
restraint,  holding  to  general  laws  and  avoiding  specific 
details.  Some  form  of  cosmical  evolution  is  now  gen- 
erally granted  and  the  heavens  are  swept  by  gigantic 
telescopes  which  linger  on  the  nebulae,  in  the  hope  that 
accurate  measurement  will  show  that  these  apparently 


INFLUENCE  ON  RECENT  SCIENCE        77 

chaotic  masses  are  slowly  changing  into  the  more  stable 
form  of  stellar  systems. 

Side  by  side  with  the  belief  in  atoms,  separated  from 
each  other  in  empty  space,  had  grown  up  the  directly 
contrary  idea  that  substance  is  continuous  and  space 
is  a  plenum.  This  doctrine  permits  us  to  make  no 
essential  difference  between  space  and  matter.  Space 
becomes  a  continuous  substance  unvaried,  and  so  im- 
perceptible to  our  senses,  while  matter  is  merely  a 
localized  variation  of  this  same  substance  of  such  a 
nature  as  to  make  it  perceptible.  And  it  is  significant 
of  these  two  systems,  that  although  they  begin  with 
contradictory  premises,  they  both  lead  to  the  same 
conclusions  after  apparently  rigorous  deductions. 

The  doctrine  of  continuity  owes  its  rise  to  Hera- 
clitus  and,  amongst  the  Greeks,  was  most  highly  de- 
veloped by  Aristotle.  They  announced  this  postulate 
because  the  notion  that  a  body  can  attract  another 
through  an  intervening  vacuum  and  cause  it  to  move 
introduces  an  occult  or  inexplicable  idea.  Our  experi- 
ence teaches  us  that  motion  results  only  from  a  push  or 
impact  between  bodies  actually  in  contact.  But  it  is 
quite  evident,  that  in  refusing  to  accept  a  force  which 
acts  contrary  to  our  experience,  which  all  goes  to  show 
that  a  material  link  is  necessary  to  produce  motion 
between  bodies,  they  fell  into  as  serious  a  difficulty, 
for  they  were  compelled  to  create  an  occult  substance 
to  serve  as  the  material  link  between  bodies,  and  occult 


78          THE  LIMITATIONS  OF  SCIENCE 

variations  in  it  for  the  bodies  themselves.  As  explana- 
tions of  phenomena  both  ideas  are  occult,  but  not  to 
the  same  degree.  We  know,  for  a  fact,  that  there  is 
an  attractive  force  between  bodies  of  sensible  size, 
although  we  cannot  explain  its  cause,  and  we  can 
in  our  imaginations  transfer  a  like  form  to  bodies  of 
an  insensible  size  with  some  probability  of  truth.  But 
the  postulation  of  a  plenum  of  continuous  substance  and 
of  variations  in  it,  which  affect  us  as  matter,  is  wholly 
occult  since  we  have  no  experience  from  sensible  mat- 
ter to  guide  us ;  in  fact,  both  plenum  and  its  variations 
always  have  characteristics  assigned  to  them  directly 
contrary  to  the  evidence  of  our  senses. 

The  history  of  scientific  theory  is  a  record  of  the 
conflict  between  these  rival  ideas  of  continuity  and  dis- 
continuity of  substance.  While  the  atomistic  school 
has  frequently  had  the  advantage,  since  the  time  of 
Descartes  the  doctrine  of  the  continuity  of  matter  has 
persisted  in  some  form,  and  at  the  present  time  is 
again  established  as  the  basis  of  physical  theory. 
Nevertheless,  the  cosmical  system  as  deduced  by  Des- 
cartes from  this  hypothesis  of  a  plenum  has  suffered 
shipwreck  and  comparatively  few  think  it  profitable  to 
study  it  in  detail.  Before  we  adopt  his  principles  and 
discard  his  conclusions,  it  is  at  least  advisable  to  see 
whether  his  errors  lie  in  the  principles  themselves  or 
in  the  inability  of  Descartes  to  derive  true  conclusions 
from  correct  principles.  Fortunately,  we  have  in  the 


INFLUENCE  ON  RECENT  SCIENCE        79 

Discours  de  la  Methode,  in  the  Principia  Naturae,  and 
in  the  many  letters  of  Descartes  an  unusually  com- 
plete record  of  his  principles,  his  method,  and  his  con- 
clusions. 

In  character,  training,  and  opportunities,  few  if  any 
philosophers  have  been  better  equipped  for  their  task 
than  Descartes.  As  has  been  said  of  him,  "he  is  a 
type  of  that  spirit  of  science  to  which  erudition  and  all 
the  heritage  of  the  past  seem  but  elegant  trifling."  He 
believed  and  acted  on  the  opinion  that  no  scientific 
knowledge  is  attainable  unless  men  doubt ;  unless  they 
put  aside  authority  and  rely  on  their  own  experience. 

Descartes  has  in  his  Principia  Naturae  set  forth 
with  specious  simplicity  the  causes,  laws,  and  the  phe- 
nomena of  the  universe  as  he  finds  them.  Geometry 
is  to  be  the  ruler  or  at  least  the  vicegerent,  and  no 
substance  will  be  discussed  except  such  as  may  be 
divided,  figured,  and  moved  according  to  the  laws 
which  geometers  hold  to  govern  quantity,  nor  will 
any  proposition  be  considered  proved  unless  it  has 
been  deduced  with  such  evidence  as  would  suffice  for  a 
mathematical  demonstration.  With  vexatious  incon- 
sistency, he  then  destroys  the  force  of  this  admirable 
introduction  by  carefully  warning  us  not  to  consider 
his  premises  true  or  his  conclusions  conformable  to 
fact,  since  his  scheme  is  really  an  hypothesis  or  sup- 
position as  to  what  might  be  and  not  what  is.  This 
caution  is  usually  attributed  to  his  fear  lest  he  should 


80          THE  LIMITATIONS  OF  SCIENCE 

arouse  the  hostility  of  the  Church  and  suffer  a  penalty 
similar  to  that  which  had  just  overwhelmed  Galileo. 
His  own  plea  was  that  he  valued  peace  more  than  the 
spread  of  his  opinions  and  also  that  he  had  always 
been  a  good  Catholic  and  bowed  to  the  authority  of 
the  Church,  even  when  its  decrees  were  contrary  to  his 
reason.  But  it  is  also  possible  that  doubts  arose  in 
his  own  mind  as  his  system  developed  and  that  when 
he  found  it  necessary  to  compromise  with  the  rigorous 
principles  he  had  announced,  he  tried  to  disarm  criti- 
cism by  the  plea  that  after  all  he  was  really  concerned 
only  with  a  fictitious  world. 

At  all  events,  while  the  laws  of  the  heavens  were 
under  consideration,  he  permitted  this  veil  of  unreality 
to  remain  very  thin;  for  he  knew  the  Church  wisely 
allowed  considerable  latitude  of  thought  concerning 
those  regions  of  space  which  apparently  contained  no 
subjects  to  Catholicism,  and  he  felt  scientifically  safe 
in  a  field  where  verification  by  experiment  was  only 
beginning  to  be  advocated.  But  the  case  was  altered 
when  he  came  to  discuss  terrestrial  laws  and  phe- 
nomena, for  here  both  Church  and  experience  held 
sway  and  must  be  conciliated.  In  this  field  Descartes, 
mindful  probably  of  both  of  these  perils,  relied  on  the 
same  hypothesis,  but  to  placate  the  Church  he  insisted 
that  it  was  to  be  understood  only  in  a  most  figurative 
sense,  because  we  know  that  God  created  the  earth, 
finished  and  perfect,  as  revealed  in  the  Mosaic  account; 


INFLUENCE  ON  RECENT  SCIENCE        81 

and  to  disarm  scientific  criticism,  his  postulates  he  de- 
clared to  be  fictions,  but  in  some  way  without  depart- 
ing from  correct  mathematical  deductions,  his  conclu- 
sions were  similar  to  experience. 

It  would  be  difficult  to  understand  from  these  con- 
tradictory statements  what  was  Descartes's  real  opinion 
of  his  scheme.  But  he  has  this  answer  in  another  part 
of  his  Principia,  an  answer  which  carries  conviction. 
Since  we  have  an  idea  of  perfection,  we  have  also 
the  certainty  of  the  existence  of  God,  or  an  all-perfect 
Being.  And  because  this  God  is  justice  itself,  if  the 
principles  laid  down  by  him  are  evident,  if  the  con- 
sequences are  founded  on  mathematical  laws,  and  if 
the  deductions  agree  with  experience,  it  would  be 
ascribing  injustice  to  God  to  believe  that  the  causes  of 
the  effects  are  false.  Now  observe  how  far  Descartes 
believes  he  has  fulfilled  these  conditions:  "  je  ne  pense 
pas  qu'on  doive  recevoir  d'autres  principes  en  la 
Physique,  ni  mesme  qu'on  ait  raison  d'en  souhaiter 
d'autres,  que  ceux  qui  sont  icy  expliquez" 

Descartes  has  recorded  for  us  how  he  arrived  at  the 
postulates  from  which  he  developed  his  natural  laws. 
Having  previously  laid  aside  preconceived  ideas,  he 
found  that  to  doubt  is  the  first  and  only  means  of 
knowledge;  we  can  doubt  the  existence  of  everything 
except  that  which  doubts,  therefore  that  which  doubts 
or  thinks,  exists.  Whence  he  derives  the  principle 
that  our  thoughts  and  the  things  we  have  an  idea  of, 


82  THE  LIMITATIONS  OF  SCIENCE 

are  real  and  objective  to  us.  However,  by  such  a  proc- 
ess we  do  not  obtain  a  knowledge  of  things  themselves, 
but  only  of  their  attributes.  Hence,  the  final  reality 
must  be  those  attributes  which  are  inseparable  from  our 
conception  of  all  phenomena,  and  there  should  be 
some  one  essential  attribute  which  may  be  used  to 
designate  things  in  general.  Thus  hardness,  while  it  is 
an  attribute,  is  not  essential,  for  a  body  moving  at 
the  same  speed  as  ourselves  does  not  give  us  the  sensa- 
tion of  hardness.  After  careful  consideration  he  found 
that  simple  extent  in  length,  breadth,  and  thickness  is 
the  one  attribute  common  and  essential  to  all  mat- 
ter. Not  only  is  this  true,  but  the  extent  of  matter  is 
identical  with  the  extent  of  space :  "  The  same  extent  in 
length,  breadth,  and  thickness,  which  constitutes  space, 
constitutes  a  body;  and  the  difference  between  them 
lies  in  this,  that  we  attribute  to  a  body  a  particular  and 
limited  extent  which  changes  position  with  the  body  as 
it  moves,  and  that  we  attribute  to  space  an  extent  so 
general  and  so  vague  that  when  we  remove  from  a  cer- 
tain space  the  body  which  occupied  it  we  do  not  think 
we  have  transported  the  extent  with  it ;  meanwhile  the 
extent  of  the  body  remains  of  the  same  size,  of  the 
same  figure,  and  has  changed  position  with  respect  to 
the  body  only  as  we  determine  position  by  other 
bodies." 

The  reason,  according  to  Descartes,  why  we  have 
been  led  to  believe  that  substance  is  different  from 


INFLUENCE  ON  RECENT  SCIENCE        83 

space,  and  that  it  consists  of  atoms  either  in  a  vacuum 
or  in  a  non-material  medium,  is  the  property  known  as 
expansion  and  contraction.  As  an  illustration,  he  in- 
stances a  sponge,  which  changes  size  but  not  character 
when  its  pores  are  filled  with  water.  Here  we  have  a 
change  of  size  from  the  change  of  position  of  sponge- 
matter,  the  two  kinds  being  of  the  same  essence.  So 
the  change  of  volume  of  any  body  is  due  to  a  change 
of  position  of  matter-substance  produced  by  a  change 
of  space-substance,  which  also  are  essentially  the  same 
and  differ  only  in  accidental  qualities. 

Furthermore,  since  we  cannot  imagine  a  space  so 
great  that  there  cannot  be  a  greater,  or  so  small  that 
it  cannot  be  divided,  then  as  matter  is  essentially  the 
same  as  space,  it  too  must  be  indefinitely  great  in  ex- 
tent and  indefinitely  divisible. 

This  is  a  very  complicated  way  of  getting  back  to 
one's  starting  point.  He  says  first,  that  substance  is 
extension  and  then  that  space  is  extension,  but  since 
extension  is  everywhere  and  space  is  nowhere  vacuous, 
a  body  is  a  body. 

Having  discussed  the  nature  of  matter  in  general, 
he  then  finds  that  diversity  in  matter  and  also  its  dif- 
ferentiation from  space  can  consist  only  in  variations 
of  position  and  motion  of  small  parts  of  space  which 
are  themselves  exactly  similar.  As  corollaries  to  this 
definition,  it  follows  that  there  can  be  neither  absolute 
position  nor  absolute  motion.  To  determine  the  posi- 


84          THE  LIMITATIONS  OF  SCIENCE 

tion  and  motion  of  a  body  we  must  use  some  other  body 
as  a  point  of  reference.  But  in  this  system,  all  space  is 
capable  of  motion  and,  in  fact,  is  in  rapid  motion,  and 
with  no  possible  stationary  reference  point  all  positions 
and  motions  are  merely  relative.  This  question  of  abso- 
lute motion  has  been  the  subject  of  much  discussion  in 
the  last  few  years,  as  certain  phenomena  of  light  re- 
quire that,  granting  a  luminiferous  ether,  it  must  be 
absolutely  stationary.  And  experiments  have  been  de- 
vised to  determine  whether  we  can  measure  the  absolute 
velocity  of  matter  with  respect  to  the  ether.  As  in  all 
experiments  involving  the  ether,  the  results  are 
nugatory. 

Nor,  in  the  theory  of  Descartes,  can  there  be  action 
at  a  distance,  for  matter  is  continuous  and  all  motion 
is  the  result  of  a  push  or  impact.  Motion,  therefore, 
he  defines  as  the  transference  of  a  part  of  matter  or  of 
a  body  from  the  neighborhood  of  those  which  touch  it 
immediately,  and  which  we  consider  at  rest,  to  the 
neighborhood  of  others.  And  since  all  space  is  full 
of  matter,  or  rather  is  matter,  each  body  is  so  fashioned 
that  it  can  never  occupy  a  greater  or  a  less  space,  nor 
can  any  other  body  occupy  the  space  while  it  is  there; 
therefore  if  a  body  move  to  another  position,  it  must 
displace  an  occupant;  and  this,  another;  so  that  every 
motion  results  in  a  closed  ring  of  moved  bodies,  each 
finally  occupying  the  space  left  by  its  previous  occu- 
pant. 


INFLUENCE  ON  RECENT  SCIENCE        85 

These  postulates  of  Descartes,  that  space  is  a  plenum 
and  motion  the  result  of  an  impact,  required  him  to 
oppose  such  theorists  as  Gassendi  who  were  advocat- 
ing the  atomic  theory  and  an  occult  attractive  force  in 
matter  as  its  cause  of  motion.  It  thus  became  of  prime 
importance  for  him  to  formulate  laws  of  impact  and 
motion.  This  was  an  extremely  difficult  problem,  espe- 
cially so  as  the  available  knowledge  of  the  phenomena 
of  impact  and  motion  was  very  deficient  and,  such 
as  it  was,  indicated  that  friction  produced  an  uncom- 
pensated  diminution  of  velocity.  With  great  care  and 
in  minute  detail,  he  announced  such  laws  as  would,  in 
his  opinion,  maintain  constant  the  total  quantity  of 
motion  or  momentum  of  the  universe  in  spite  of  fric- 
tion. That  is,  such  laws  as  would  transfer  the  loss  of 
motion  of  one  body  by  impact  to  an  equivalent  increase 
of  another.  These  laws  are: 

God  in  his  omnipotence  created  matter  with  motion 
and  rest. 

If  a  body  move  twice  as  fast  as  another  twice  as 
great,  the  quantity  of  motion  of  the  two  is  the 
same. 

All  bodies,  which  move,  tend  to  move  in  straight 
lines  and  can  change  their  direction  only  by  encounter- 
ing others. 

If  a  moving  body  strike  another  of  greater  mo- 
mentum (plus  fort)  than  itself,  it  loses  none  of  its 
motion  and  if  it  strikes  another  with  a  less  momentum 


86          THE  LIMITATIONS  OF  SCIENCE 

(plus  foible)  which  it  can  move,  it  loses  as  much  mo- 
tion as  it  gives  to  the  other. 

Then  seven  other  laws  of  impact  of  less  importance 
follow,  which  it  is  not  necessary  to  quote,  as  Huygens 
later  showed  that  all  eight  were,  for  the  most  part, 
erroneous. 

In  spite  of  the  fact  that  Descartes,  without  verifica- 
tion, invented  the  laws  of  motion  of  bodies  and  of 
their  impact,  yet  we  must  recognize  that  he  sought 
and  found  one  of  the  great  scientific  principles ;  that  un- 
less the  universe  is  tending  to  a  state  of  uniform  rest 
through  dissipation  of  motion  by  friction,  some  active 
property  of  matter  must  be  conservative  in  addition  to 
its  quantity.  While  his  particular  law  of  the  con- 
servation of  momentum  was  erroneous,  yet  it  is  un- 
doubtedly the  progenitor  of  the  law  finally  enunciated 
by  von  Helmholtz  and  now  generally  accepted,  that  the 
total  quantity  of  energy  remains  constant. 

With  these  general  principles  settled,  the  nature  of 
space  and  matter,  and  its  conservation  of  quantity  and 
action,  we  shall  defer  criticism  and  describe  the  vari- 
ous kinds  and  phenomena  of  matter  as  nearly  as  pos- 
sible in  the  sense  of  Descartes. 

We  are  to  suppose  that,  in  the  beginning  of  time, 
God  divided  all  space  or  substance  into  equal  parts, 
which,  contrary  to  the  chaos  pictured  by  poets  and 
philosophers,  had  been  previously  in  perfect  uniformity 
and  rest.  Out  of  these  primordial  particles  of  space 


INFLUENCE  ON  RECENT  SCIENCE        87 

were  fashioned  all  the  small  constituent  parts  of  mat- 
ter which  now  compose  not  only  all  terrestrial  and 
celestial  bodies  but  also  the  interstellar  spaces.  While 
we  do  not  know  the  actual  size  of  these  particles,  as 
they  were  originally  or  as  they  are  now  after  they  have 
suffered  changes,  some  growing  smaller  by  division  and 
others  larger  by  the  accretion  of  many  into  one  from 
causes  which  will  be  described  later;  yet  their  first 
size  must  have  been  the  exact  average  of  all  the  con- 
stituent particles  now  comprising  the  universe.  God 
also  caused  these  primordial  particles  to  move,  and 
with  equal  force  in  two  diverse  fashions :  each  to  rotate 
about  its  own  center  to  form  the  constituent  elements 
of  the  interstellar  spaces,  or,  as  Descartes  calls  them, 
the  fluid  body  of  the  heavens,  and  many  to  revolve  to- 
gether about  common  axes,  creating  vortices  whose 
centers  are  the  nuclei  of  the  sun  and  fixed  stars  in  the 
heavens.  The  velocity  of  this  uniform  motion  was  the 
average  of  all  the  diverse  motions  existing  now,  so 
that  the  quantity  of  motion  or  momentum  has  remained 
constant  throughout  all  time. 

Although  these  primordial  particles  were  of  equal 
size  and  motion,  they  could  not  have  been  spherical  in 
shape,  since  a  pile  of  spheres  does  not  fill  a  space  and 
there  must  be  no  vacuum.  But  whatever  their  initial 
figure  may  have  been,  they  have  in  the  course  of  time 
become  exact  spheres.  The  cause  of  this  change  of 
shape  is,  that  the  force,  by  which  they  were  first  moved, 


88  THE  LIMITATIONS  OF  SCIENCE 

was  sufficiently  great  to  separate  them  from  each  other, 
and  was  therefore  great  enough  to  knock  off  their 
angular  edges  and  corners  because  of  the  concussions 
of  their  future  impacts.  The  result  of  such  a  constant 
attrition  is  well  known  to  be  that  the  body  approaches 
the  figure  of  a  sphere,  just  as  the  pebble  on  the  seashore 
becomes  round  from  the  grinding  of  the  waves  and  its 
fellows. 

This  action  gives  rise  to  three  fornis  of  matter  which 
constitute  the  universe,  and  whose  various  forms  of  ag- 
gregation and  proportions  of  mixture,  with  their  re- 
sulting varieties  of  motion,  account  for  all  the  diversi- 
fied kinds  and  attributes  of  matter  and  space. 

The  first  kind  of  matter  is  the  cosmic  dust  of  attri- 
tion or  the  little  fragments  resulting  from  the  above 
mentioned  collisions.  They  are  excessively  small  and 
have  acquired  enormous  velocities,  because  the  larger 
particles,  from  which  they  were  split  off,  have  con- 
strained them  to  move  faster  than  themselves  through 
the  narrow  and  tortuous  paths  formed  by  their  inter- 
stices, just  as  air  in  a  whistle  moves  the  faster,  the 
smaller  the  orifice  from  which  it  issues.  They  are 
also  so  numerous,  so  various  in  size,  and  so  irregular 
of  shape,  that  there  are  always  sufficient  of  them  ready 
to  hand  to  fill  exactly  any  space  which  might  other- 
wise be  left  vacuous  by  the  arrangement  and  motion  of 
their  parent  sphericules. 

The  second  elementary  kind  includes  all  the  rest  of 


INFLUENCE  ON  RECENT  SCIENCE        89 

matter  and  space,  whose  least  parts  are  spheres  and 
smaller  than  any  body  we  know,  but  they  are  much 
larger  than  matter  of  the  first  kind. 

There  is  also  a  third  kind  of  matter  formed  by  con- 
glomerate masses  of  the  other  two  kinds,  which  have 
become  so  linked  and  interlaced  together  as  to  be  in- 
separable, at  least  by  human  means.  The  pores  of 
these  masses  are  filled  with  the  spheres  of  the  second 
kind  and  the  fragments  of  the  first  kind. 

The  first  kind  of  matter  forms  the  sun  and  the  fixed 
stars ;  the  second  kind  is  the  material  for  the  so-called 
empty  spaces  of  the  heavens;  and  the  third  is  the  basis 
of  the  diversified  bodies  composing  the  earth,  the 
planets,  and  the  comets. 

As  stated  before,  this  elementary  matter  was  origi- 
nally endowed  with  two  kinds  of  motion:  the  rotation 
of  each  particle  about  its  own  axis  and  the  revolution 
of  many  about  a  common  axis,  forming  a  vortex  or 
whirlpool.  Descartes  then  portions  out  the  heavens 
so  that  the  axis  of  a  vortex  will  pass  through  the  center 
of  each  star,  including  the  sun.  The  outer  limit  of 
each  vortex  extends  so  far  in  every  direction  as  to 
touch  the  confines  of  each  of  the  neighboring  star- 
vortices  ;  in  this  manner  all  space  is  occupied  by  them, 
rushing  about  their  several  axes  with  a  velocity  de- 
creasing as  the  distance  from  the  axis  increases.  It 
is  naturally  a  problem  of  great  intricacy  to  place  these 
immense  vortices  so  that  they  will  not  interfere  with 


90          THE  LIMITATIONS  OF  SCIENCE 

each  other's  motion,  and  he  spends  much  labor  and 
great  ingenuity  in  describing  the  possible  inclinations 
of  axes  and  directions  of  motion  of  such  a  system, 
but  not  satisfactorily. 

The  sun  and  stars,  as  they  now  are,  were  not  created 
contemporaneously  with  the  vortices  but  were  a  gradual 
growth  from  them.  When  more  dust  of  attrition  was 
ground  from  the  rotating  matter  of  a  vortex  than  was 
sufficient  to  fill  the  interstices  of  this  matter,  it  began 
to  flow  toward  the  center  and  along  the  axis  of  the 
vortex,  gradually  forming  there  a  nucleus,  ires  subtil  et 
ires  liquide;  namely,  a  luminous  star.  According  to 
Descartes's  idea,  which  in  spite  of  his  contempt  for  au- 
thority he  borrowed  from  Aristotle  and  the  schoolmen, 
these  stellar  masses,  consisting  of  matter  of  the  first 
kind  exclusively,  are  pure  celestial  fire,  which  is  thus 
an  entity  and  of  all  things  the  most  fluid  and  so  vio- 
lently agitated  as  to  be  able  to  disintegrate  the  most 
solid  bodies.  Fire  of  itself  does  not  need  to  be  replen- 
ished but  only  seems  to  need  replenishment,  because  the 
particles  of  a  terrestrial  fire  are  constantly  flying 
away  and  being  dissipated,  and  so  must  be  renewed  by 
others  derived  from  the  pores  of  gross  combustible 
bodies  and  of  air;  but  in  celestial  fires  there  is  no  need 
of  external  replenishment  because  the  steady  stream 
of  fire-substance,  flowing  of  its  own  accord  to  the 
center  of  the  vortex,  maintains  a  constant  supply. 
Alas,  that  the  spectroscope  should  show  us  that  our  sun 


INFLUENCE  ON  RECENT  SCIENCE        91 

and  the  stars  are  not  this  pure  elemental  fire  but  merely 
heated  matter  of  a  terrestrial  nature.  Such  havoc  does 
experiment  play  with  a  grandiose  hypothesis.  We 
may,  however,  pass  over  difficulties  impossible  to  have 
been  foreseen  by  Descartes,  since  many  men  of  science 
still  think  an  hypothesis  valuable  if  it  escapes  con- 
temporaneous troubles,  and  of  these  there  are  always 
an  abundance. 

Between  these  star  centers  lie  the  great  interstellar 
spaces  which  some  believe  to  be  vacuous  but  which 
Descartes  supposes  are  packed  with  matter  of  the  sec- 
ond kind.  The  interstices,  which  would  otherwise 
exist  between  these  little  spheres,  are  filled  with  matter 
of  the  first  kind.  And  all  together  they  rush  around 
common  axes  to  form  the  vast  heavenly  vortices  with 
a  velocity  enormous  but  less  than  that  of  the  celestial 
fire  of  the  stars. 

This  accounts  for  all  the  universe  except  those  parts 
occupied  by  terrestrial  and  planetary  bodies,  which 
are  composed  mostly  of  matter  of  the  third  kind.  The 
constituent  parts  of  this  kind  of  matter,  as  stated  be- 
fore, consist  of  agglomerated  masses  of  the  other  two 
kinds,  whose  pores  are  filled  with  matter  of  the  first 
and  second  kinds  still  in  their  simple  state.  Accord- 
ing to  the  relative  proportions  and  various  arrange- 
ments of  these  three  constituents,  we  distinguish  all  the 
different  bodies  which  are  classed  as  solids,  liquids, 
and  gases.  Of  these,  solid  bodies  are  those  whose  least 


92          THE  LIMITATIONS  OF  SCIENCE 

parts  are  made  of  closely  packed  and  intricately  ar- 
ranged particles,  which  can  move  with  respect  to  each 
other  but  very  slightly,  if  at  all.  The  spaces  between 
the  constituent  parts  of  a  liquid  are  greater  and  contain 
a  larger  proportion  of  the  subtle  elements  than  solids ; 
while  gases  have  their  particles  so  separated  that  they 
approach  fire  in  their  freedom  of  motion.  As  he 
quaintly  puts  it :  a  body  is  a  fluid  when  it  is  divided  in 
many  little  parts  which  are  free  to  move  separately  in 
various  ways,  and  it  is  hard  when  all  its  parts  are  so 
interlaced  that  there  is  no  action  capable  of  separating 
them.  Cohesion  in  hard  bodies  is  caused  by  the  lack 
of  motion  of  their  constituent  parts,  for  no  cement 
could  be  harder  than  rest,  which  is  the  quality  the  most 
contrary  to  motion.  He  does  not  tell  us  how  to  inter- 
lace and  twist  a  number  of  spheres  and  irregular 
fragments  together,  so  as  to  form  compact  and  in- 
extricable units  of  matter.  To  anyone  but  a  great 
philosopher  they  would  remain  ropes  of  sand. 

Descartes  had  spent  much  time  investigating  the  ex- 
perimental laws  and  phenomena  of  light  and  with 
notable  success.  One  of  his  greatest  ambitions  was 
evidently  to  explain  the  nature  of  light  and  the  mode  of 
its  transmission,  for  he  discusses  these  in  great  detail 
in  his  Principia  and  refers  to  his  solution  of  the  prob- 
lem constantly  in  his  letters  with  much  complacency. 

As  noted,  the  substance  of  the  sun  and  stars  is  like 
fire  in  respect  to  its  motions;  for  there  is  nothing 


INFLUENCE  ON  RECENT  SCIENCE        93 

more  agitated  than  fire  which  can  disintegrate  even 
solid  matter  into  its  smallest  parts,  and  then  carry  them 
away.  So  we  should  believe  that  the  matter  of  the 
sun  is  celestial  fire,  very  fluid  and  agitated,  carrying 
off  with  it  particles  of  the  heavens.  Although  matter 
of  the  first  kind  is  constantly  rushing  along  the  axis 
toward  the  center  of  the  vortex,  yet,  when  it  approaches 
that  point,  it  experiences  a  tendency  to  fly  out  to  the 
equatorial  surface  because  of  its  centrifugal  force. 
The  effort,  not  only  of  the  little  spheres  of  the  second 
kind  but  also  of  the  fragmentary  particles  of  the  first 
kind,  to  leave  the  center  of  a  stellar  vortex,  constitutes 
light.  While  all  particles  of  a  vortex  may  tend  to 
move  away  from  the  center  because  of  their  cen- 
trifugal force,  yet,  since  they  are  packed  like  balls  in 
a  cup,  they  cannot  really  move  and  so  only  tend  to 
move.  Just  as  when  a  sufficient  hole  is  made  in  the 
bottom  of  a  cup  filled  with  balls,  one  of  them  drops 
through  and  all  the  balls  lying  within  an  inverted  cone 
settle  down;  so  it  is  with  light,  if  any  particle  in  space 
tends  to  move,  this  tendency  or  pressure  is  instantly 
transmitted  to  any  distance  along  straight  lines,  which 
come  not  only  from  the  center  of  a  luminous  body  but 
also  from  all  points  in  its  superficies.  If  we  attempted 
to  discuss  details,  we  should  find  ourselves  worried 
and  baffled  between  this  tendency  to  move  in  a  plenum 
and  the  real  motions  of  balls  in  a  cup  containing  free 
spaces  between  them.  But  there  is  little  use  in  fretting 


94          THE  LIMITATIONS  OF  SCIENCE 

over  such  a  detail,  when  the  entire  conception  is  not 
light  nor  anything  resembling  light.  Descartes  may, 
perhaps,  prove  that  this  tendency  to  move  proceeds 
in  straight  lines  and  would  be  reflected  and  refracted 
in  agreement  with  the  laws  of  light;  that  the  inter- 
stellar spaces  would  be  transparent;  that  terrestrial 
bodies  would  vary  from  transparency  to  opacity  ac- 
cording to  the  greater  proportion  and  complexity  of 
matter  of  the  third  kind  in  their  composition;  but  the 
mechanism  of  all  this  is  far  more  obscure  and  com- 
plicated than  the  phenomena  it  attempts  to  elucidate. 

This  theory  of  light  advanced  in  the  Principia  was, 
in  a  sense,  supported  by  the  rather  meager  experimental 
knowledge  then  existing,  and  seems  at  first  plausible. 
But  examined  critically,  and  with  the  mind  no  longer 
awed,  or  perhaps  hypnotized,  by  Descartes's  sweep  of 
imagination  and  his  power  of  making  words  seem  to 
express  clear  ideas  when  they  really  do  not,  his  cause 
of  light  is  found  to  be  as  arbitrary  as  the  fiat  lux  of  a 
God,  and  its  effects  mere  confusion.  In  fact,  it  is  the 
unavoidable  weakness  of  any  such  hypothesis,  and  a 
very  irritating  and  tantalizing  weakness,  that  the  words 
used  apparently  express  things  we  can  understand,  and 
yet  when  we  try  to  visualize  these  things,  stripped  of 
technical  and  intricate  verbiage,  the  mind  has  received 
no  clear  impression. 

And  here  we  have  a  splendid  example  of  an  hypoth- 
esis, whose  foundations  now  seem  ridiculous;  whose 


INFLUENCE  ON  RECENT  SCIENCE        95 

laws  are  not  correct  generalizations;  and  whose  con- 
clusions are  unlike  the  phenomena  of  nature;  which, 
nevertheless,  anticipates  an  idea  to  be  advanced  again, 
after  a  century  and  a  half.  This  hypothesis  of  light 
contains,  as  a  corollary,  the  germ  of  the  kinetic  theory 
of  heat.  He  discards  the  notion,  which  then  generally 
prevailed,  that  heat  was  a  sort  of  mysterious  substance 
called  caloric,  for  which  indeed  there  was  no  place  in 
his  universe,  and  defines  it  as  the  oscillatory  agitation 
of  terrestrial  particles,  set  up  by  the  pressure  of  light. 
The  pores  of  such  bodies  are  tortuous,  and  the  pressure 
of  light  on  one  end  of  such  a  gross  and  irregularly 
shaped  particle  may  be  greater  than  on  the  other  end 
and  so  cause  a  tipping  motion.  Such  a  tilt  would  give 
an  oscillatory  motion  to  a  particle,  similar  to  a  violin 
string  when  bowed,  and  he  believed  its  momentum 
affects  us  as  heat.  An  oscillation  of  this  sort  would 
communicate  itself  to  neighboring  particles  and  there- 
fore explains  the  conduction  of  heat  from  one  part  of 
a  body  to  another;  also,  it  accounts  for  the  expansion 
of  bodies  by  heat,  since  vibrating  particles  usually  re- 
quire more  space  than  quiescent  ones;  but,  on  the 
other  hand,  they  might  be  so  shaped  and  arranged  as  to 
occupy  less  space,  when  in  motion,  and  such  a  body 
should  contract  if  heated.  Such  an  effect  was  unknown 
at  that  time,  but  we  ought  to  claim  that  it  was  bril- 
liantly verified  when,  in  later  years,  water  was  ob- 
served to  contract  when  heated  from  zero  to  four 


96          THE  LIMITATIONS  OF  SCIENCE 

degrees  Centigrade.  Not  to  contradict  known  phe- 
nomena, and  to  anticipate  some  unknown  ones,  is  held 
to  be  the  justification  of  such  hypotheses;  by  this 
standard  Descartes  was  successful  as  few  others  have 
been.  Yet,  if  we  compare  the  splendid  advances  which 
he  made  in  science  by  his  experimental  discoveries  and 
his  application  of  mathematics  to  physical  laws,  to  the 
mass  of  falsehood  in  his  metaphysical  schemes  by 
which  he  dominated  science  and  which  still  flourish 
in  the  metaphysical  theories  now  in  vogue,  we  can 
hardly  tell  whether  he  has  benefited  or  done  harm  to 
science  by  his  labors.  Possibly  no  labor  is  too  great, 
if  by  it  we  arrive  at  ever  so  little  truth,  but  no  one  can 
believe  that  this  medieval  conception  of  light  and  heat 
induced  his  successors  to  seek  for  a  possible,  but  unex- 
pected, contraction  of  water.  Surely  the  converse  is 
the  case  and  his  metaphysical  divination  was  purely 
specious ;  the  phenomena  were  discovered  without  any 
reference  to  his  theory  and  probably  without  even  a 
knowledge  of  it,  and  now,  if  we  wish,  we  may  use  them 
as  a  buttress  for  Descartes's  tottering  edifice. 

The  fourth  and  last  book  of  the  Principia  is  devoted 
to  an  explanation  of  the  natural  phenomena  of  the 
earth.  At  first  the  earth  was  a  small  stellar  vortex, 
composed  of  matter  of  the  first  kind  only,  and  was  one 
of  fourteen  satellary  nuclei  located  in  our  larger  solar 
vortex.  Gradually  the  less  subtile  parts  of  its  mass 
attached  themselves  together  and  formed  spots  or 


INFLUENCE  ON  RECENT  SCIENCE        97 

crusts  on  its  surface,  similar  to  sun-spots,  a  phe- 
nomenon then  recently  made  known  by  the  telescope. 
Sun-spots,  because  of  the  superior  agitation  of  solar 
matter,  are  broken  up  and  disappear,  but  the  earth- 
spots  formed  more  rapidly  than  they  dissipated,  finally 
covering  its  surface  with  a  thick  crust  of  many  layers, 
composed  of  what  he  called  matter  of  the  third  kind. 
This  crust  diminished  the  motion  of  the  terrestrial 
vortex  and  finally  destroyed  it  altogether,  so  that  the 
earth  with  its  atmosphere  and  its  obscure  bodies  de- 
scended toward  the  sun  to  the  place  it  now  occupies. 

With  the  earth  in  its  proper  position  and  with  the 
beginnings  of  diversity  in  its  composition,  Descartes 
was  free  to  employ  the  remainder  of  his  treatise  to  the 
description  of  the  character  of  each  aggregation  of 
elementary  matter  necessary  to  form  the  various 
chemical  substances;  the  proportions  and  velocities  of 
the  three  kinds  of  matter  to  produce  forces,  such  as 
cohesion,  weight,  etc.,  and  the  different  geo-physical 
phenomena,  such  as  winds,  rain,  and  earthquakes.  It 
is  amazing  how  much  he  passes  before  our  eyes,  and 
how  ingeniously  he  links  his  ideas,  giving  to  them  the 
appearance  of  the  greatest  plausibility. 

There  is  little  profit  in  discussing  these  at  length, 
for  if  the  conclusions  of  the  hypothesis  were  absurd 
when  applied  to  those  regions  of  space  about  which  we 
even  yet  know  little,  they  become  grotesque  when  con- 
nected with  matter  which  we  can  investigate  experi- 


98          THE  LIMITATIONS  OF  SCIENCE 

mentally.  Besides  our  thesis  is  with  such  methods  in 
general,  and  in  this  respect  only  is  a  study  of  Des- 
cartes's  system  useful,  as  it  is  his  method  which  still 
flourishes  in  the  theories  of  physics  and  of  other  sci- 
ences. He  is  to  be  admired  in  this  respect;  when 
he  had  once  outlined  his  premises  and  his  method,  he 
deduced  his  conclusions  as  rigorously  as  possible,  and 
compared  them  consistently  with  experience;  whereas 
it  has  become  the  custom  now  to  alter  postulates  when- 
ever their  conclusions  point  to  error,  with  the  result 
that  it  is  most  difficult  to  outline  a  consistent  and  in- 
vidual  modern  theory.  If  we  study  modern  scientific 
theories  we  find  that  the  postulates  are  as  metaphysical, 
if  not  more  so,  than  those  of  Descartes.  They  are 
stated  with  much  assurance,  but  as  the  conclusions  un- 
fold themselves,  we  begin  to  notice  a  certain  hesitation 
and  a  desire  to  limit  the  discussion  to  a  small  and  re- 
lated class  of  phenomena.  Or  if  an  excursion  is  made 
into  a  wider  field,  lack  of  confidence  increases  and  usu- 
ally results  in  a  modification  and  confusion  of  the 
postulates.  If  Descartes's  theory  may  be  illustrated  as 
a  tree  with  all  its  conclusions  branching  out  from  a 
single  idea  as  a  stem,  our  present  state  of  physics  is 
like  a  thicket  of  bushes  with  many  stems  so  concealed 
and  interwoven  that  the  parent  stem  of  any  branch 
cannot  be  distinguished. 

I  have  sketched  the  most  elaborate  and  comprehen- 
sive hypothesis  ever  developed  in  the  name  of  science, 


INFLUENCE  ON  RECENT  SCIENCE        99 

which,  if  it  means  anything  to  mankind,  is  his  best 
expression  of  verity  and  fact.  Yet  we  see  Descartes, 
an  illustrious  man  of  science,  devoting  his  talents  to 
the  exposition  of  an  openly  confessed  fiction.  And  his 
reputation  rests  on  the  belief  that  he  has  spun  a  web 
of  fancy  so  subtly  that  it  could  deceive  us.  While 
additional  knowledge  has  been  acquired  by  us,  no  one 
has  shown  that  modern  theorists  have  discovered  a 
method  different  and  more  trustworthy  than  that  of 
Descartes.  We  recognize  that  many  of  the  laws  he 
formulated  are  false  and  that  most  of  his  facts  have 
been  corrected  or  disproved,  but  we  should  remember 
that  modern  hypotheses  also  are  developed  as  a  means 
of  attacking  unexplored  regions  of  science  where  our 
own  knowledge  is  either  meager  or  false.  For  ex- 
ample, he  felt  it  necessary  to  find  a  cause  for  the 
recently  discovered  sun-spots  and  then  extended  its 
action  so  as  to  change  a  vortex  into  a  primitive  ter- 
restrial planet.  A  better  knowledge  of  these  spots  on 
the  sun  proves  that  his  whole  reasoning  was  false,  or 
shall  I  say  childish.  But  was  it  less  plausible  at  that 
time  or  even  less  childish  than  is  now  our  most  recent 
theory;  that  an  atom  of  matter  is  a  system  of  cor- 
puscles, each  of  which  is  a  unit  of  free  negative  elec- 
tricity moving  with  the  velocity  of  light,  and  that  this 
denatured  bit  of  electricity  is  nothing  but  a  localized 
strain  in  an  ethereal  plenum.  Let  us  examine  such  a 
postulate  as  we  would  a  similar  statement  if  it  had  been 


ioo        THE  LIMITATIONS  OF  SCIENCE 

made  by  Descartes.  We  may  admit  with  Lord  Kelvin 
that  we  know  nothing  about  the  real  nature  of  elec- 
tricity. We  do  know  experimentally  that  electricity 
seems  to  be  associated  always  with  matter ;  the  greatest 
velocity  we  have  caused  or  observed  any  body  of  an 
appreciable  size  to  have,  is  one  thousand  eight  hun- 
dred times  less  than  the  speed  of  light.  An  ethereal 
plenum  is  certainly  only  a  matter  of  imagination,  and 
the  conception  of  matter  as  a  strain  in  this  imaginary 
plenum  is  hardly  a  clear  idea.  So  it  seems  that  the 
facts  supporting  our  modern  postulates  regarding  the 
nature  of  substance  are  as  meager  and  doubtful,  and 
our  ideas  as  obscure  for  our  purpose,  as  those  of  Des- 
cartes were  for  his. 

On  the  contrary,  it  is  no  exaggeration  to  say  that 
there  probably  never  lived  a  man  better  equipped  than 
Descartes  to  make  and  to  defend  an  hypothesis;  his 
scientific  skepticism,  his  freedom  from  the  trammels 
of  authority,  his  devotion  and  skill  in  experimental 
work,  his  determination  to  submit  his  ideas  to  the 
rigorous  logic  of  mathematical  analysis  in  which  he 
was  the  leader  of  his  age,  were  admirable  qualities  for 
such  a  purpose.  A  man  who  doubts  even  his  own 
existence,  is  not  likely  to  adopt  other  ideas  lightly.  To 
strip  matter  of  every  quality  except  mere  extension;  to 
abolish  every  cause  of  phenomena  except  linear  mo- 
tion and  the  impact  of  bodies,  both  of  which  are 
capable  of  the  most  accurate  experimental  investiga- 


INFLUENCE  ON,  R£C£N?f:  SCIENCE:  -\  101 

tion;  is  to  attempt  the  limit  of  simplicity  in  scientific 
procedure.  Why  Descartes  chose  such  a  postulate  as 
the  criterion  of  matter,  is  directly  traceable  to  his 
fundamental  dictum:  cogito,  ergo  sum.  If  his  own 
existence  is  real  only  because  of  thought,  and  if  mind 
or  thought  be  the  criterion  of  all  reality,  form  replaces 
substance,  and  the  extent  of  matter  is  its  essential 
quality.  Although  Descartes  went  further  in  this  di- 
rection than  most  men  of  science  are  willing  to  go, 
yet  he  has  imposed  his  method  on  science  to  the  present 
day  and  we  are  still  industriously  building  worlds  as  we 
think  them  to  be. 

Dazzling  as  the  system  of  Descartes  appears  when 
viewed  as  a  whole,  it  has  a  foundation  of  sand  and  an 
imaginary  rather  than  a  substantial  superstructure. 
Consider  his  statements:  space  or  matter  is  infinite  in 
extent  and  continuous  in  character,  and  in  the  begin- 
ning it  was  divided  in  equal  parts  which  were  then 
moved  with  a  force  sufficient  to  separate  them.  If 
matter  fills  all  space,  or  rather  is  space,  where  was  the 
additional  space  to  permit  of  this  separation  and  what 
then  filled  the  interstices  between  the  separated  parts? 
Again,  the  impact  and  grinding  of  particle  on  par- 
ticle are  supposed  to  have  reduced  them  to  uniform 
spheres  and  the  dust  of  this  attrition  then  served  to 
fill  the  spaces  left  in  such  a  pile  of  spheres.  This 
dust  is  of  all  shapes  and  so  fine  that  there  is  always 
at  hand  just  the  proper  quantity  to  fill  any  space  be- 


102       :    H     LIMIT-ATIO-NS  OF  SCIENCE 

tween  the  spheres.  It  really  amounts  to  endowing 
these  cosmic  fragments  with  the  intelligence  of  Leib- 
nitzian  monads;  if  impact  and  grinding  produced  them, 
why  are  they  also  not  true  spheres?  The  sand  on  the 
seashore  is  as  spherical  as  the  pebbles.  Then  too,  if 
the  original  parts  of  space  were  reduced  in  size  by  at- 
trition, why  did  they  attain  a  certain  size  and  then 
cease  to  be  worn  away?  Or  are  we  to  suppose  that 
the  whole  universe — earth,  stars,  and  interstellar  spaces 
— are  still  grinding  themselves  away  until  some  day  all 
its  parts  will  be  reduced  to  the  size  of  the  cosmic  dust 
which  he  calls  fire  ?  We  might  go  still  further  and  let 
the  universe  actually  grind  itself  into  nothing,  and 
simply  vanish. 

But  even  if  we  showed,  step  by  step,  that  the  scheme 
not  only  was  not  true,  but  even  not  capable  of  resisting 
the  most  cursory  criticism,  we  should  be  met  by  the 
answer;  that  as  knowledge  increases,  details  which  are 
erroneous  will  be  abandoned  and  new  ones  substituted 
which  better  approximate  to  the  truth.  This  counter- 
criticism  seems  aside  from  the  question;  it  would  be 
strange  if  the  efforts  made  to  discover  new  phenomena 
and  laws,  and  to  correct  false  ones,  did  not  increase  our 
knowledge.  But  is  this  aim  furthered  by  such  hypo- 
thetical systems,  which  attempt  to  describe  the  mechan- 
ism of  these  phenomena  and  laws,  and  which,  at  bot- 
tom, assume  that  their  authors  are  the  creators  of  the 
universe  and  not  observers  of  one  whose  laws  and 


INFLUENCE  ON  RECENT  SCIENCE       103 

phenomena  are  independent  of  them;  a  confusion  of 
subjective  ideality  and  objective  reality?  Also  how- 
ever it  advances,  our  knowledge  of  nature  will  always 
be  so  inadequate  that  the  very  announcement  of  a 
system  of  nature  should  cause  us  to  suspect  it  of  being 
etched  out  by  fancy,  and  to  be  useless  as  an  aid  to 
scientific  investigation.  Nor  can  we  find  a  system 
which  does  not  transgress  constantly  the  limitations  of 
science,  and  it  is  safe  to  say  none  will  ever  be  proposed 
which  will  not  transgress  them,  because  it  is  the  desire 
for  such  a  system  that  is  false,  and  not  its  develop- 
ment. 

On  the  other  hand,  the  discovery  and  verification 
of  phenomena  should  be  unreservedly  advocated,  also 
their  classification  into  laws  and  even  the  restricted  use 
of  hypothesis.  But  the  latter  has  come  to  have  two 
meanings  in  scientific  usage.  The  word  hypothesis 
very  frequently  signifies  a  law  which  has  been  pretty 
accurately  expressed  and  verified  by  available  experi- 
ence, but  which  still  does  not  embrace  some  phenomena 
believed  to  be  related  to  it,  or  is  contradicted  by  some 
others ;  for  example,  the  law  of  conservation  of  energy 
was  an  hypothesis  in  this  sense,  until  the  discovery  of 
the  mechanical  equivalent  of  heat  proved  that  the  me- 
chanical energy,  apparently  lost  in  every  action  by 
friction,  was  accurately  balanced  by  the  thermal  energy 
produced  by  the  friction.  Such  hypothetical  reason- 
ing is  quite  warranted ;  in  fact  a  law  or  hypothesis  of 


104         THE  LIMITATIONS  OF  SCIENCE 

this  sort  should  always  be  announced  as  soon  as  a  con- 
siderable number  of  facts  point  to  its  probable  truth; 
such  tentative  laws  always  direct  attention  to  the  phe- 
nomena involved  and  stimulate  research. 

But  hypothesis  in  the  other  sense  does  not  gradually 
crystallize  into  law  as  our  knowledge  increases.  No 
information,  however  greater  than  ours  at  present, 
will  ever  advance  Descartes's  hypothesis  a  step  closer 
to  a  law.  We  shall  never  have  any  data  about  his 
three  kinds  of  matter,  his  nature  of  free  space,  etc.;  we 
learn  constantly  more  about  the  action  of  light  but 
we  still  drift  confusedly  and  without  a  guide  between 
his  apparatus  of  pressures,  Newton's  corpuscles,  and 
Huygens's  waves;  the  latest  treatise  on  optics  now 
states  that  we  may  have  to  mix  together  all  three  of 
them. 

The  system  of  Descartes  will  fascinate  anyone  who 
surrenders  himself  to  its  spirit  and  scope,  but  illusion 
is  not  the  function  of  science.  Nor  can  I  find  any  more 
accurate  and  just  criticism  of  this  and  all  other 
hypotheses  than  that  given  by  Bolingbroke :  "  The 
notion  Descartes  entertained  and  propagated,  that  there 
is,  besides  clear  ideas,  a  kind  of  inward  sentiment  of 
evidence,  which  may  be  a  principle  of  knowledge,  is, 
I  suppose,  dangerous  in  physical  inquiries  as  well  as 
in  abstract  reasoning.  He  who  departs  from  the 
analytic  method,  to  establish  general  propositions  con- 
cerning the  phenomena  on  assumptions,  and  who  rea- 


INFLUENCE  ON  RECENT  SCIENCE      105 

sons  from  these  assumptions,  afterwards  on  inward 
sentiments  of  knowledge,  as  they  are  called,  instead  of 
clear  and  real  ideas,  lays  aside,  at  once,  the  only  sure 
guides  to  knowledge.  This  Descartes  did  very  widely 
in  his  construction  of  a  world,  and  yet  by  dint  of  genius 
he  gave  a  great  air  of  simplicity  and  plausibility  to  his 
hypothesis,  and  he  knew  how  to  make  even  geometry 
subservient  to  error.  .  .  .  The  plenum  of  Descartes 
is  well-nigh  destroyed ;  many  of  his  laws  of  motion  are 
shown  to  be  false;  the  mills  that  served  to  grind  his 
three  elements  are  demolished :  and  his  fluid  matter  in 
which,  as  in  a  torrent,  the  planets  were  carried  around 
the  sun,  whilst  a  similar  motion  in  the  particular  vortex 
of  every  planet  impelled  all  bodies  to  the  center,  is 
vanished.  Notwithstanding  all  this,  how  slowly,  how 
unwillingly  have  many  philosophers  departed  from 
the  Cartesian  hypothesis?" 

That  Bolingbroke  was  mistaken  when  he  says  that 
the  plenum,  the  vortices,  and  all  the  other  apparatus 
of  Descartes  have  been  destroyed,  can  be  readily  seen 
by  reading  any  modern  treatise  on  physics. 

But  he  was  vividly  correct  in  the  larger  and  more 
important  part,  when  he  finds  that  all  such  hypotheses 
are  based  on  an  inward  sentiment  of  truth  and  not  on 
clear  and  real  ideas.  An  inward  sentiment  of  knowl- 
edge is  and  must  be  the  final  guide  of  anyone  who  em- 
ploys this  hypothetical  method,  for  how  can  anyone 
have  clear  and  real  ideas  about  such  things  as  tran- 


io6         THE  LIMITATIONS  OF  SCIENCE 

scend  experience?  And  amongst  the  many  following 
this  method,  what  man  can  be  the  arbiter  to  declare 
which  one  has  been  gifted  by  a  divine  power  with  the 
true  inward  sentiment  of  knowledge  ? 


CHAPTER  IV 
THE  SCIENTIFIC  METHOD 

The  truth  of  science  has  ever  had  not  merely  the  task  of 
evolving  herself  from  the  dull  and  uniform  mist  of  ignorance, 
but  also  that  of  repressing  and  dissolving  the  phantoms  of  the 
imagination. — FARADAY. 

IF  we  are  compelled  to  revert  to  old  and  supposedly 
discarded  systems  of  thought  when  we  attempt  to 
make  new  hypothetical  systems,  we  should  inquire 
whether  we  are  really  advancing  the  theory  of  science 
by  that  method.  Is  it  true  that  Descartes  reaches  in 
his  wonderful  clarity  of  expression  the  highest  attain- 
ment in  speculative  thought?  Even  in  the  then  little 
cultivated  subjects  of  electricity  and  magnetism,  his 
imagination  did  not  fail  him  and  he  drew  a  picture  of 
the  field  of  force  about  a  magnet  which  is  strikingly 
like  those  in  modern  treatises.  And  to  explain  elec- 
trical attraction,  he  supposed  bodies  to  contain  little 
filaments  of  his  elementary  matter  which  were  crowded 
out  when  the  bodies  were  rubbed  together.  These  fila- 
ments attached  themselves  like  lines  of  force  to  neigh- 
boring bodies.  When  the  rubbing  was  stopped  they 
retracted  and  so  drew  the  electrified  bodies  together. 
If  we  modernize  this  explanation,  we  have  a  fair  state- 

107 


io8         THE  LIMITATIONS  OF  SCIENCE 

ment  of  Faraday's  lines  of  force.  Faraday  believed 
that  when  a  body  is  electrified  the  space  about  it  is 
filled  with  lines  of  electric  force  which  are  stretched  in 
the  direction  of  their  length  and  experience  a  pressure 
at  right  angles  to  their  direction.  This  idea,  or  rather 
the  modification  of  it  by  Maxwell,  who  was  able  to  as- 
sign quantitative  values  to  those  forces  which  corre- 
spond with  the  laws  of  electrical  attraction  and  repul- 
sion, is  expressed  more  precisely.  But  qualitatively: 
that  is,  in  telling  us  what  electricity  is ;  why  it  is  pro- 
duced by  friction;  and  what  lines  of  force  are;  the 
modern  statement  is  no  more  definite  than  that  of  Des- 
cartes. It  is  a  mistake,  however,  to  suppose  he  pos- 
sessed a  unique  power  of  formulating  hypothesis;  other 
early  writers  attained  eminence  in  this  respect.  Thus 
Sir  Thomas  Browne  thought  that  electric  effluvia  (the 
prevailing  name  for  force)  behave  like  threads  of 
syrup  which  elongate  and  contract  and  so  produce  at- 
traction; Von  Guericke  stated  that  bodies  contain  efflu- 
via which  emanate  from  them  according  to  their  nature 
and  form  an  electric  field  of  force.  In  agreement  with 
these  opinions,  we  are  taught  to-day  that  the  best  way 
to  consider  lines  of  force  is  to  picture  an  electrified 
body  as  one  surrounded  by  stretched  elastic  bands.  As 
a  diagram  to  show  the  direction  of  motion  of  an  at- 
tracted body,  and  as  a  name  for  the  quantity  of  force, 
this  conception  of  elastic  lines  of  force  is  accurate  and 
convenient.  But  Faraday  and  Maxwell  went  far  be- 


THE  SCIENTIFIC  METHOD  109 

yond  this,  as  they  gave  to  them  a  concrete  reality. 
This  conception  still  persists,  although  Sir  J.  J.  Thom- 
son showed  years  ago  that  no  known  system  of  me- 
chanical forces  would  keep  such  a  system  of  force-lines 
in  equilibrium  and  Professor  Lorentz  now  says  they 
cannot  really  exist  but  are  fictions  of  the  imagination. 
It  seems  rather  futile,  if  such  be  the  normal  his- 
tory of  hypothetical  models,  to  inflict  on  us  the  labor  of 
learning  abstruse  hypotheses  which  continually  revamp 
old  metaphysical  terms  and  merely  dress  them  up  in 
new  transcendental  symbols.  It  is  a  valuable  exercise 
to  strip  hypotheses  of  their  technical  phraseology;  to 
change  those  words  which  deceive  our  minds  into  be- 
lieving that  a  clear  idea  has  been  conveyed,  when,  in 
fact,  they  have  merely  been  wrenched  from  any  real 
significance.  Thus  Sir  Oliver  Lodge  says  that  the 
ether  is  very  massive.  This  definition  at  once  increases 
our  belief  in  its  reality  since  it  conveys  the  impression 
that  the  ether  is  tangible  and  impenetrable,  something 
like  a  vast  globe  of  rock.  And  we  must  stop  to  think 
before  we  realize  that  whatever  the  ether  may  be,  it 
must  be  just  the  opposite  to  our  ordinary  ideas  of  mas- 
sive things.  Or  what  clear  idea  is  conveyed  by  Pro- 
fessor Einstein's  definition  that  vacuous  space  contains 
radiant  energy  which  is  an  entity  of  the  same  kind  as 
matter  ?  Does  he  not  add  to  the  difficulty  when  he  says 
further,  that  the  difference  between  a  vacuum  and  the 
ether  is  that  the  latter  is  a  vacuum  transmitting  radiant 


no        THE  LIMITATIONS  OF  SCIENCE 

energy  and  possesses  a  light  vector.  What  right  has  he 
to  insinuate  into  our  minds  that  a  vacuum  may  contain 
something  and  still  be  a  vacuum  ?  He  does  this  by  a 
play  on  the  word  "  energy,"  which  he  permits  us  to 
think  of  in  the  ordinary  sense  as  an  attribute  of  matter 
and  at  the  same  time  states  implicitly  to  be  a  distinct 
entity.  We  are  inclined  to  pass  lightly  over  the  second 
statement  because  we  tacitly  think  of  a  light  vector  as 
a  geometrical  line;  the  substance  of  such  a  line  is  too 
intangible  to  give  a  distinct  shock  to  the  reason.  But 
if  we  put  this  definition  to  a  simple  test,  we  easily  see 
how  futile  it  is.  Say  to  anyone,  that  a  golf  ball  in  its 
flight  is  not  a  thing  of  rubber  and  paint  but  a  complex 
of  energy;  and,  that  this  is  true  because  the  moving 
golf  ball  has  a  motion  vector  and  consequently  changes 
vacuous  space  into  ether.  How  quickly  such  a  state- 
ment about  a  familiar  action  would  be  recognized  as  an 
absurdity.  I  presume  that  the  reason  why  we  like  to 
indulge  in  these  phantoms  of  the  imagination  is  be- 
cause we  still  hate  to  confess  our  ignorance.  But  it  is 
a  pity  that  science  thus  lurks  in  the  mists. 

We  can  easily  follow  modern  hypothesis  as  it  pro- 
gresses into  transcendental  symbolism.  Sir  Joseph 
Larmor  and  Professor  Lorentz  wish  to  define  elec- 
tricity so  that  it  may  be  measured.  They  adopt  the 
hypothetical  method  to  a  limited  degree.  Thus,  they 
each  postulate  the  atom  of  matter.  They  next  assume 
each  atom  to  consist  of  a  multitude  of  positively  and 


THE  SCIENTIFIC  METHOD  in 

negatively  electrified  particles  which  revolve  in  orbits. 
Except  to  say  that  these  particles  may  be  a  modifica- 
tion of  an  ether,  they  avoid  explicit  details.  Their 
method  of  exposition  is  still  the  classic  method  of 
mechanics.  When  they  try  to  explain  certain  lately 
discovered  and  obscure  phenomena,  they  merely  show 
that  they  could  be  satisfied  by  supposing  the  dimen- 
sions of  bodies  to  be  influenced  by  their  motion.  At 
this  point  they  wisely  refrain  from  further  explana- 
tions. Next  we  find  that  Professor  Einstein  definitely 
changes  electrical  particles  into  particles  of  electricity 
and  matter  into  complexes  of  energy.  He  speaks  so 
confidently  of  his  ability  to  visualize  electricity  and 
energy  that  we  feel  our  own  inability  to  do  so  results 
from  a  pitiful  lack  of  intelligence.  At  this  point  he 
clinches  the  whole  matter  and  explains  the  changes  of 
the  dimensions  of  moving  bodies  by  introducing  the  oc- 
cult idea  that  light  is  an  entity  which  moves  in  space 
with  a  constant  velocity.  It  is  a  far  cry  from  the  induc- 
tive method  of  science  which  attempts  to  build  general- 
izations on  experience,  thus  to  make  the  whole  concrete 
world  conform  to  so  abstract  an  idea  as  the  constancy 
of  the  velocity  of  light  in  space.  Nor  does  he  hesitate 
to  found  physical  science  on  the  paradox,  that  motion 
cannot  be  absolute  but  the  motion  of  light  is  absolute. 
Then  Professor  Minkowski  goes  a  step  further.  He 
accepts  all  these  ideas  and  then  treats  them  symbol- 
ically. To  deduce  conclusions  from  these  postulates, 


ii2         THE  LIMITATIONS  OF  SCIENCE 

he  uses  mathematical  equations  as  if  there  were  four 
dimensions  to  space.    The  mathematician  can  employ 
equations  which  contain  four  or  any  number  of  vari- 
ables, but  the  physicist  who  desires  to  deal  with  an 
objectively  real  universe  and  also  to  be  intelligible  is 
forced  to  limit  himself  to  the  three  dimensions  which 
correspond  to  his  powers  of  measurement  of  length, 
,     breadth,  and  depth.    Lastly,  Professor  Lewis  confuses 
scientific  method  utterly  by  arbitrarily  assuming  which 
quantities  in  an  equation  shall  be  treated  as  variable 
and  which  as  constant.     Thus  he  says,  if  the  mo- 
mentum of  a  body  changes,  let  us  suppose  that  this 
happens  not  because  its  motion  changes  but  because  we 
shall  consider  its  mass  variable.     Of  course  anyone 
can  say,  let  us  consider  the  universe  to  act  as  he  wishes. 
But,  after  all,  what  is  the  use  when  no  one  believes  it 
does  ?    Is  it  any  wonder  that  a  gulf  is  growing  not  only 
between  men  of  science  and  the  rest  of  the  world,  but 
also  between  theorists  and  those  who  are  still  willing 
to  submit  their  imagination  to  experience?     Such  a 
gulf  is  certain  to  continue  so  long  as  theorists  are 
willing,  and  even  anxious,  to  ignore  common  sense  and 
the  facts  gained  by  patient  and  exact  experimenta- 
tion. 

It  is  true  that  my  criticism  of  scientific  method  has 
been  so  far  purely  destructive.  And  in  that  admission 
may  lie  the  ineffectiveness  of  the  argument  to  many. 
Some  will  say  that  however  weak  and  vacillating  the 


THE  SCIENTIFIC  METHOD  113 

hypothetical  method  may  have  been,  yet  it  is  the  custom 
of  thought  and  in  spite  of  it  or  even,  in  some  way,  be- 
cause of  it,  scientific  truth  has  nobly  expanded,  dis- 
pelling ignorance  and  subjugating  natural  forces.  But 
because  knowledge  advances,  objection  should  not  be 
made  to  a  protest  against  what  tends  to  embarrass  a 
more  rapid  advance.  Such  a  protest  is  the  value  of 
destructive  criticism.  The  reason  why  scientific  knowl- 
edge advances  in  spite  of  hypotheses,  those  phantoms 
of  the  imagination,  is  because  hypothesis  rarely  pre- 
cedes experiment.  If  we  examine  the  work  of  the 
experimenter  of  to-day,  we  find  he  still  goes  on  calmly 
working  with  apparatus  and  using  it  with  the  common 
sense  idea  that  he  is  using  real  objective  matter  in  spite 
of  the  attempt  of  the  theorist  to  make  it  an  attribute 
of  energy  or  electricity.  The  conclusions  derived  from 
experiment  and  laws  may  be  discussed  and  condemned 
or  approved  according  as  they  support  a  fashionable 
hypothesis,  but  scientific  hypothesis  is  much  like  re- 
ligious dogma :  although  it  may  protest,  yet  in  the  end 
it  swerves  around  to  accept  all  new  facts.  And  in  a 
short  time  the  despised  fact  is  cited  as  a  pillar,  or  at 
least  as  a  flying  buttress  of  the  hypothesis. 

While  it  is  not  possible  to  draw  a  definite  boundary 
line  between  the  regions  of  physics  and  metaphysics, 
still  we  may  do  so  in  a  general  way  by  saying  that  the 
domain  of  physics  is  concerned  with  the  discovery  of 
phenomena  and  the  formulation  of  natural  laws  based 


H4         THE  LIMITATIONS  OF  SCIENCE 

on  postulates  which  are  determined  by  experience  and 
generally  accepted  as  true;  the  causes  of  phenomena 
and  the  discussion  of  the  postulates  of  science  lie  in  the 
province  of  the  metaphysician.  This  differentiation  in 
method  of  thought  cannot  be  rigidly  adhered  to  since 
the  boundary  line  is  more  or  less  obscure,  and  is  liable 
to  considerable  displacement  as  a  science  advances ;  but 
the  acceptance  of  this  principle  would  prevent  much  of 
the  confusion  which  has  been  introduced  into  science 
by  writers  who  have  not  recognized  it  to  be  a  general 
,  rule.  For  example,  the  principle  of  relativity  is  not 
strictly  a  physical  law  but  the  expression,  in  mathe- 
matical symbols,  of  the  general  philosophical  law  of  the 
finite  nature  of  the  human  mind  which  has  been  ac- 
cepted for  centuries.  Again,  the  discussion  of  the 
shape  of  the  atom  or  electron  is  not  a  physical  prob- 
lem, as  it  is  incapable  of  verification  by  experience. 
This  does  not  mean  that  such  questions  should  not  be 
discussed,  but  the  method  of  their  discussion  and  the 
results  obtained  are  properly  the  method  and  results 
of  metaphysics  and  are  not  in  the  category  of  physical 
phenomena  and  laws. 

In  the  first  place,  men  of  science  must  accept  the 
existence  of  an  objective  universe,  whose  phenomena 
and  laws  are  external  to  our  intelligence  and  will. 
But,  since  the  interpretation  of  phenomena  is  sub- 
jective and  thus  conditioned  by  our  intelligence  and 
will,  scientific  laws  are  governed  by  the  mathematical 


THE  SCIENTIFIC  METHOD  115 

theory  of  probability,  or  the  consensus  of  opinion  of 
the  greatest  number,  working  with  the  greatest  care. 

The  basic  laws  of  physics  are  the  laws  of  continuity 
and  conservation,  and  the  law  of  cause  and  effect. 
Unless  we  believe  that  something,  matter,  energy,  or 
both,  remains  unchanged  in  amount  and  has  a  continu- 
ous existence  however  changed  in  appearance,  and  un- 
less phenomena  can  be  repeated,  we  have  no  certainty 
of  knowledge  and  no  means  of  communicating  ideas 
to  others.  The  discussion  of  the  reality  of  these  laws 
may  be  left  to  the  philosopher,  but  I  dare  say,  however 
he  decides,  they  will  continue  to  be  accepted  by  man- 
kind generally. 

The  universality  and  application  of  these  and  other 
laws  should  be  rigidly  limited  to  experience  by  the 
physicist.  The  law  of  conservation  requires  that  the 
quantity  of  matter  and  energy  is  either  infinite,  which 
means  nothing,  or  that  there  is  an  exact  interchange 
in  quantity  in  every  action.  This  belief  is  expressed 
in  Newton's  law  that  to  every  action  there  is  an  equal 
and  contrary  reaction.  But  it  is  evident  that  conserva- 
tion, as  a  scientific  law  which  may  be  verified,  is  limited 
to  a  very  small  category  of  observations  and  is  only  ap- 
proximate for  them.  Thus  we  know  nothing  of  the 
total  amount  of  energy  radiated  from  the  sun  or  where 
it  goes.  Hypothesis  here  shows  considerable  vacilla- 
tion. Some  assert  that  the  universe  is  infinite  and  so 
the  radiation  never  reaches  a  boundary;  others  say 


ii6        THE  LIMITATIONS  OF  SCIENCE 

that  the  universe  is  so  filled  with  matter  that  no  straight 
line  can  be  drawn  from  the  sun  without  reaching  an 
obstacle  and  so  radiant  energy  is  reflected  back  and 
forth ;  again  the  universe  may  be  finite  in  size  and  its 
boundary  may  be  a  reflecting  surface.  These  hypotheses 
are  evidently  futile  speculations  and  no  support  to  the 
law  which  we  have  been  driven  to  accept  and  shall 
continue  to  accept  until  personal  observation  shows  re- 
sults which  increasingly  depart  from  the  law. 

So,  too,  the  law  of  cause  and  effect  is  a  generaliza- 
tion from  few  observations  and  neither  supports  nor  is 
supported  by  hypothesis.  While  we  can  never  hope  to 
establish  such  a  law,  it  is  nevertheless  a  necessary  gen- 
eralization, or  scientific  deduction  becomes  meaningless. 
The  fact  is,  the  phenomena  of  the  universe  do  not  re- 
veal themselves,  as  a  whole,  in  any  regular  sequence 
of  cause  and  effect ;  and  our  theories,  based  on  such  a 
law,  show  such  a  complex  tangle  as  to  be  quite  beyond 
our  power  to  interpret.  The  law  involves  time,  and 
past  time  at  that;  and  the  successive  causes  of  an  ob- 
served phenomenon,  if  carried  back  in  any  logical 
sequence,  soon  widen  out  into  an  incomprehensible 
maze  and  vanish  in  the  obscurity  of  the  past.  The 
most  beautiful  and  perfect  example  of  this  law  is  the 
belief  in  organic  evolution.  Yet  on  what  meager  and 
inaccurate  observations  it  rests.  Everyone  believes  in 
some  such  law,  but  no  one  can  point  out  the  sequence 
of  cause  and  effect,  and  its  rigorous  development  leads 


THE  SCIENTIFIC  METHOD  117 

to  absurdity.  Mathematically  it  is  a  law  of  geometri- 
cally decreasing  types  which  reduce  finally  to  a  single 
protoplasm.  If  we  adopt  the  hypothetical  method,  we 
should  discuss  the  origin  of  this  protoplasm.  To  say 
it  was  made  by  God,  is  not  scientific.  Lord  Kelvin 
offers  an  hypothesis  (although  one  would  suppose  he 
was  joking  if  the  context  were  not  so  serious)  when 
he  suggests  that  the  original  protoplasm  may  have 
fallen  on  the  earth  from  some  celestial  body!  How- 
ever we  are  to  consider  such  an  extraordinary  state- 
ment, we  do  know  that  Maxwell  tried  to  support  the 
hypothesis  of  pangenetic  evolution  by  the  futile 
method  of  estimating  the  number  of  molecules  in  a 
germ.  The  question  with  him  was  whether  there  were 
enough  molecules  to  form  miniature  organs  and  parts 
of  the  mature  object  into  which  the  germ  would  ex- 
pand. 

Another  illustration  may  be  given  to  show  that  as 
soon  as  we  extend  our  laws  beyond  the  point  where 
verification  is  possible,  we  merely  cause  confusion. 
Certain  experiments  indicate  that  the  apparent  mass  of 
a  body  changes  when  it  moves  in  an  electric  field.  The 
law  shows  that  the  mass  should  become  infinite  when 
the  velocity  equals  that  of  light.  This  conclusion  has 
been  accepted  as  the  basis  of  an  hypothesis  that  the 
velocity  of  light  is  a  maximum  limit  to  motion.  Such 
a  belief  is  not  only  pure  hypothesis  but  it  is  contrary 
to  the  conclusions  of  other  hypotheses.  If  this  hypo- 


ii8        THE  LIMITATIONS  OF  SCIENCE 

thetical  method  is  generally  applicable  it  is  necessary 
to  explain  gravitational  action  also  as  due  to  some 
form  of  motion;  Laplace  has  shown  that  the  motion 
involved  requires  a  velocity  many  times  that  of  light. 

Our  most  fundamental  perception  of  an  external 
universe  seems  attainable  from  our  sense  perception  of 
force.  The  muscular  sense  of  effort  is  apparently  the 
simplest  and  most  general  mechanical  notion  we  have, 
and  in  the  opinion  of  the  masters  of  the  science  our 
idea  of  force  is  adequate  to  serve  as  the  basis  of  so 
exact  a  science  as  physics.  Yet,  when  we  attempt  to 
make  force  serve  as  a  fundamental  measure  of  phe- 
nomena, we  have  found,  since  the  time  of  Newton,  that 
it  is  not  so  convenient  as  mass  and  acceleration.  Mo- 
tion is  further  divisible  into  a  measurement  of  length 
and  time.  It  is  therefore  customary  to  reduce  all  our 
complex  observations  into  combinations  of  the  funda- 
mental units  of  mass,  length,  and  time  instead  of  force. 
The  idea  of  force  being  thus  associated  in  our  minds  as 
an  attribute  of  matter,  we  postulate  the  objective 
reality  and  conservation  of  matter  and  assume  the 
fundamental  attribute  of  matter  to  be  its  mass  or 
inertia.  M.  Hannequin  expresses  this  idea  clearly 
when  he  says  that  nothing  in  a  mechanical  sense  exists 
except  masses  in  motion. 

We  shall  next  assume  length,  mass,  and  time  to  be 
the  fundamental  units  of  measure.  These  quantities 
are  continuous  or,  at  least,  are  indefinitely  divisible. 


THE  SCIENTIFIC  METHOD  119 

The  continuity  of  space  and  time  is  generally  accepted ; 
without  this  belief  it  is  impossible  to  establish  the 
geometrical  laws  of  figure  founded  on  the  point,  line, 
and  surface  or  the  analytical  laws  of  motion  derived 
from  the  calculus.  The  only  exception  I  know  to 
this  postulate  is  Professor  Planck's  theory  of  quanta, 
in  w7hich  motion  may  occur  in  jumps.  But  the  divisi- 
bility of  matter  is  not  usually  supposed  to  be  infinite. 
Indeed,  the  denial  of  this  assertion  is  the  foundation 
of  all  atomic  theories.  Yet  it  is  difficult  to  see  how 
mathematics  can  be  anything  but  abstract  logic,  or  how 
it  can  be  applied  to  physical  problems  unless  this  third 
fundamental  quantity,  which  is,  as  it  were,  the  con- 
necting link  between  the  abstract  and  the  concrete,  be 
also  indefinitely  divisible.  It  is  only  by  the  postulate 
of  the  indefinite  divisibility  of  mass  that  we  may  pass 
from  the  mathematical  laws  of  pure  motion  (kine- 
matics) to  the  physical  laws  of  the  motion  of  bodies 
(dynamics).  How,  otherwise,  can  we  replace  finite 
bodies  by  mathematical  centers  of  inertia?  In  this 
connection  Sir  Joseph  Larmor  says :  "  The  difficulty  of 
imagining  a  definite  uniform  limit  of  divisibility  of 
matter  will  always  be  a  philosophical  obstacle  to  an 
atomic  theory,  so  long  as  atoms  are  regarded  as  dis- 
crete particles  moving  in  empty  space.  But  as  soon  as 
we  take  the  next  step  in  physical  development,  that  of 
ceasing  to  regard  space  as  mere  empty  geometrical 
continuity,  the  atomic  constitution  of  matter  (each 


120        THE  LIMITATIONS  OF  SCIENCE 

ultimate  atom  consisting  of  parts  which  are  incapable 
of  separate  existence,  as  Lucretius  held)  is  raised  to 
a  natural  and  necessary  consequence  of  the  new  stand- 
point." This  is  clearly  an  attempt  to  reconcile  the  two 
antinomies  of  continuity  and  discontinuity,  which  are 
usually  attached  to  the  names  of  Descartes  and  Lucre- 
tius. This  Sir  J.  Larmor  tries  to  do  by  postulating 
the  existence  of  a  true  matter,  which  is  a  continuous 
plenum  and  imperceptible  to  our  senses,  and  relegat- 
ing sensible  matter  to  the  role  of  a  mere  variation  in 
this  otherwise  changeless  plenum — making  it  an  at- 
tribute rather  than  an  entity.  If  this  definition  denies 
the  infinite  divisibility  of  matter,  it  apparently  accepts 
its  indefinite  divisibilty ;  the  atom,  as  a  variation  limited 
only  by  our  power  of  observation,  must  become  smaller 
with  each  advance  in  the  refinement  of  our  apparatus. 
Such  a  plenum  must  remain  a  pure  creation  of  the 
imagination,  and  its  existence  is  not  determinable  by 
physical  or  experimental  methods;  it  must  therefore 
be  classed  as  a  problem  for  the  metaphysician.  The 
distinction  between  atoms  continually  diminishing  in 
size  and  the  infinite,  or  at  least  indefinite,  divisibility 
of  matter  is  here  a  question  of  words — the  definition  of 
what  matter  is. 

Few  things  have  been  brought  out  more  clearly  by 
modern  physicists  than  that,  if  we  accept  the  doctrine 
of  the  continuity  and  conservation  of  energy,  either  of 
the  two,  matter  or  energy,  may  be  considered  as  the 


THE  SCIENTIFIC  METHOD  121 

fundamental  unit  from  which  the  other  can  be  derived. 
This  undoubtedly  follows  from  the  fact  that  we  have 
no  conception  of  matter  without  energy  or  of  energy 
without  matter.  But  while  it  is  thus  possible  mathe- 
matically to  make  either  of  them  a  starting-point  for 
the  explanation  of  phenomena,  the  advocates  of  ener- 
getics apparently  soon  develop  a  pronounced  tendency 
to  prefer  the  abstract  to  the  concrete  and  to  subtilize 
objective  facts  into  metaphysical  ideas.  A  science  like 
physics,  to  be  useful  and  not  merely  an  intellectual 
gymnastics,  should  preserve  in  all  its  speculations  a 
close  touch  with  the  practical  and  the  concrete — a  cer- 
tain common  sense.  The  history  of  the  science  shows 
these  advantages  have  been  obtained  most  frequently 
by  those  who  maintain  matter  and  not  energy  to  be 
a  fundamental  entity.  The  failure  of  the  mechanistic 
school  has  arisen  from  the  attempt  to  explain  the  na- 
ture of  matter,  the  cause  of  its  forces,  and  the  proper- 
ties of  atoms.  However  we  may  try  to  reason  away 
the  belief  in  the  objective  reality  of  matter,  our  minds 
persistently  cling  to  the  advantage,  and  even  neces- 
sity, of  such  a  postulate,  and  we  consciously  or  uncon- 
sciously endow  any  substitute  of  it  with  all  the  prop- 
erties of  matter,  excepting  its  name. 

Energy  is  to  be  considered  then  as  an  attribute  of 
matter  and  may  be  defined  as  the  power  to  do  work. 
It  is  customary  and  convenient  to  divide  energy  into 
two  classes,  potential  and  kinetic,  according  as  the  mat- 


122        THE  LIMITATIONS  OF  SCIENCE 

ter  concerned  appears  to  be  at  rest  or  in  motion.  Since 
attractive  forces  exist  between  all  bodies,  we  find  that 
the  idea  of  work  is  involved  whenever  the  distance 
between  bodies  is  altered  and  we  denote  this  potential 
energy  as  the  force  of  attraction  times  the  distance  be- 
tween them.  I  accept  frankly  the  idea  of  action  at  a 
distance,  not  because  it  seems  reasonable,  for  my  ex- 
perience teaches  me  that  to  cause  motion  I  must  con- 
struct a  link  between  two  bodies ;  but  the  fact  remains, 
that  both  gravitational  and  electrical  attractions  seem 
to  act  at  a  distance  and  all  attempts  made  to  explain 
them  have  so  confused  the  mind  that  the  occult  phe- 
nomenon is  less  perplexing  than  the  occult  explanation. 
In  the  majority  of  such  problems  we  can  go  no  further ; 
but  in  certain  cases,  as  for  instance  the  theory  of 
gases,  a  portion  of  the  potential  energy  due  to  the  pres- 
sure of  gases  may  be  ascribed  to  the  impact  of  small 
moving  masses  of  gases.  Even  here,  a  portion  of  the 
energy  of  the  gas  must  be  considered  as  potential  and 
incapable  of  further  explanation.  Kinetic  energy  is 
the  power  of  work  due  to  the  motion  of  bodies.  Its 
measure  is  one  half  the  moving  mass  into  the  square  of 
its  velocity.  These  two  kinds  account  for  all  the  energy 
of  material  bodies;  they  are  mutually  interchangeable 
and  their  sum  is  a  constant. 

A  third  class  of  energy  remains  to  be  discussed.  It 
is  called  radiant  energy;  its  difference  lies  in  the  fact 
that  it  is  not  associated  with  material  bodies.  Cer- 


THE  SCIENTIFIC  METHOD  123 

tain  forms  of  the  energy  of  bodies  which  we  name 
heat,  light,  etc.,  are  observed  to  appear  in  other  bodies 
although  the  space  between  them  is  devoid  of  matter. 
We  suspect  that  the  amount  of  this  energy  disappear- 
ing in  the  emitting  bodies  is  equal  to  the  amount  ap- 
pearing in  the  receiving  bodies  and  that  time  elapses 
between  the  emission  and  the  reception  of  the  energy. 
On  these  ideas  we  have  built  the  theory  that  energy 
travels  through  immaterial  space  and  in  its  transit  we 
call  it  radiant  energy.  The  conception  of  radiant 
energy  in  a  vacuum  is  a  useful  one  if  we  limit  it  to  a 
mere  quantitative  idea.  For  this  purpose  it  suffices  to 
state  the  facts  in  a  mathematical  formula  which  ex- 
presses a  continuous  passage  of  a  quantity  of  energy 
through  space  equal  to  the  amount  lost  by  the  emitting 
body.  We  thereby  generalize  the  laws  of  continuity 
and  conservation  and  of  cause  and  effect.  This  is  not 
the  custom ;  it  is  usual  to  try  to  explain  the  nature  and 
mechanism  of  radiant  energy.  This  requires  either 
that  space  be  filled  with  an  ether  to  serve  as  the  vehicle 
of  energy  or  that  energy  be  regarded  as  itself  an 
entity. 

It  has  been  the  persistent  attempt  of  physicists  for 
centuries  to  explain  this  radiant  energy  by  mechanical 
models.  And  this  effort  has  fastened  on  the  science 
an  interminable  series  of  impossible  fictitious  ethers 
and  mechanical  atoms.  The  most  indefatigable  labors 
of  the  greatest  minds  have  been  spent  to  construct  an 


124        THE  LIMITATIONS  OF  SCIENCE 

atom,  which  would  serve  satisfactorily  as  a  source  and, 
at  the  same  time,  as  a  receptacle  of  radiant  energy  and 
an  ether  which  would  transfer  it.  Not  one  of  these 
models  has  been  even  partially  adequate;  the  course  of 
the  development  has  been  steadily  from  the  simple  to 
the  complex,  from  the  concrete  to  the  abstract,  from 
the  physical  to  the  metaphysical,  until  the  most  recent 
atom  is  a  complex  more  intricate  than  a  stellar  cos- 
mogony, whose  parts  are  an  entity  called  electricity,  and 
the  ether  is  an  abstraction  devoid  of  any  mechanical 
attributes.  Out  of  all  this  controversy  we  have  gained 
the  following  facts : — Heat,  light,  and  electrical  energy, 
originating  in  one  body,  may  be  assumed  to  pass 
through  space  undiminished  and  unaugmented  to  an- 
other body.  We  can  also  express  this  energy  as  kinetic 
energy  while  it  is  associated  with  matter.  In  transit, 
since  our  experience  gives  us  no  clew  or  criterion,  we 
can  assume  as  a  formula  for  the  energy,  either  a 
periodic  motion  of  an  hypothetical  something,  called 
an  ether,  or  a  projectile  motion  of  an  hypothetical  mass- 
particle.  In  either  case,  all  we  really  do  is  to  divide 
the  initial  or  final  material  energy  into  two  mathe- 
matical quantities,  one  a  mass-factor  and  the  other  a 
velocity-factor,  and  give  to  each  such  a  value  as  to 
make  their  product  remain  a  constant.  As  a  rule,  we 
make  the  mass-factor  so  small  that  we  can  shut  our 
eyes  to  its  existence  and  imagine  anything  about  it 
we  please.  The  time  relation  is  fixed  by  experiment. 


THE  SCIENTIFIC  METHOD  125 

For  the  purposes  of  theory,  although  this  energy  ap- 
peals to  our  senses  in  the  three  forms  of  heat,  light, 
and  electricity,  which  in  their  qualitative  aspects  are 
each  fundamental  and  not  referable  one  to  another,  we 
fortunately  find  that  quantitatively  all  three  are  satis- 
fied by  one  dynamic  formula.  We  have  therefore  ob- 
tained an  adequate  quantitative  knowledge  of  energy, 
but  not  an  inkling  of  the  qualitative  coefficients  in  this 
formula. 

The  hypothesis  of  the  ether  is  an  attempt  to  accom- 
plish the  impossible.  And  while  it  is  now  generally 
admitted  that  we  cannot  create  such  a  substance  as  will 
satisfy  the  physical  requirements  of  a  transmitter  of 
radiant  energy,  still  the  ether  is  claimed  to  be  a  useful 
hypothesis.  This  utility  is  said  to  consist  in  giving  us 
a  crude  image,  in  a  mechanical  way,  of  what  occurs. 
In  other  words,  it  supports  our  innate  dislike  to  con- 
fessing complete  ignorance,  and  it  provides  a  set  of 
concrete  analogies  for  abstract  statements  and  equa- 
tions. Now  the  old  elastic  solid  and  mechanical  ether  did 
afford  us  a  concrete  image  of  a  mechanism  for  radiant 
energy,  and  we  could  speak  of  it  with  some  intelligence 
to  one  another,  because  everyone  has  a  conception  of 
an  elastic  solid.  To  be  sure,  this  solid  ether  became  a 
grotesque.  It  permitted  the  transference  of  heat  and 
light  energy,  but  only  at  the  expense  of  creating  a  kind 
of  matter  entirely  outside  of,  and  contradictory  to, 
anything  in  our  experience.  We  have  only  to  recall  the 


126        THE  LIMITATIONS  OF  SCIENCE 

properties  ascribed  to  this  ether  to  find  that  it  operated 
equally  well  if  it  had  a  density  indefinitely  great  or  one 
indefinitely  small;  if  it  were  rigid  or  if  it  were  col- 
lapsible, etc.  As  certainly  as  one  physicist  endowed  it 
with  a  property,  another  arose  who  showed  that  just 
the  opposite  property  was  equally  efficient.  Yet  we 
might  still  be  staggering  along  with  the  conviction  that 
somehow  this  supposititious  stuff  was  of  use  to  us;  at 
least  it  gave  us  a  set  of  words  conveying  some  meaning. 
But  when  Maxwell  proved  mathematically  that  a  third 
kind  of  radiant  energy  of  an  electrical  type  should  be 
looked  for,  and  when  Hertz  demonstrated  its  existence, 
no  elastic  solid  would  serve  for  all  three  kinds ;  and  so, 
for  a  time,  we  were  taught  simultaneously  the  proper- 
ties of  two  coexistent  ethers.  An  elastic  solid  and  a 
so-called  electro-magnetic  ether  in  a  single  space  were 
impossible,  and  the  former  soon  collapsed  since  it  was 
more  concrete  and  thus  more  vulnerable  to  criticism. 
Maxwell's  idea  produced  a  revolution  in  the  theory 
of  physics;  heat  and  light  remained  no  longer  a  form 
of  mechanical  waves  but  became  electro-magnetic 
waves  of  a  special  periodicity.  By  a  progressive  sub- 
tilization  we  have  now  arrived  at  Sir  J.  Larmor's  cele- 
brated definition  of  a  medium  which  will  satisfy  all 
forms  of  radiant  energy.  The  ether  is  "  a  plenum  with 
uniform  properties  throughout  all  extension,  but  per- 
meated by  intrinsic  singular  points,  each  of  which 
determines  and,  so  to  speak,  locks  up  permanently  a 


THE  SCIENTIFIC  METHOD  127 

surrounding  steady  state  of  strain  or  other  disturb- 
ance." This  ether  is  unaffected  by  any  type  of  me- 
chanical action  since  ethereal  strains  are  of  an  unknown 
kind  responding  only  to  electro-magnetic  stresses. 
This  definition  seems  general  enough  to  satisfy  the 
most  critical,  but  Professor  Einstein  goes  much  fur- 
ther. He  says  we  must  abolish  the  ether  because  the 
only  difference  between  empty  and  occupied  space  is 
that  the  latter  is  the  seat  of  an  entity,  energy,  and 
contains  a  light  vector.  Such  a  definition,  in  the  sense 
of  explaining  a  complex  idea  in  terms  of  simpler  ones, 
is  wholly  incomprehensible  and  at  the  same  time  ap- 
parently denies  and  affirms  the  existence  of  the  ether. 
But  Professor  Einstein  is  not  averse  to  paradoxes. 
These  ideas  evidently  reduce  matter  to  an  attribute  of 
electricity,  and  make  all  forces  of  the  type  called  elec- 
trical forces.  But  if  electricity  is  everything,  we  must 
inevitably  some  time  explain  pure  mechanical  actions 
in  terms  of  this  electrical  substance.  Sir  J.  Larmor 
clearly  foresees  this,  as  shown  by  his  statement :  "  The 
electric  character  of  the  forces  of  chemical  affinity  was 
an  accepted  part  of  the  chemical  views  of  Davy,  Ber- 
zelius,  and  Faraday ;  and  more  recent  discussions,  while 
clearing  away  crude  conceptions,  have  invariably 
tended  to  the  strengthening  of  that  hypothesis.  The 
mode  in  which  the  ordinary  forces  of  cohesion  could 
be  included  in  such  a  view  is  still  quite  undeveloped." 
He  thus  rather  leaves  this  question  in  the  air  by  con- 


128        THE  LIMITATIONS  OF  SCIENCE 

eluding  that  a  complete  theory  is  not  necessary.  But 
the  history  of  science  shows  that  we  shall  soon  create 
two  media  or  try  to  give  properties  to  one  which  will 
include  electrical,  chemical,  and  material  forces;  in- 
deed, this  latter  is  already  being  attempted.  If  the 
conception  of  an  elastic  solid  ether  was  admittedly  a 
fiction  of  the  mind,  and  one  impossible  to  align  with 
any  known  kind  of  matter,  the  electro-magnetic  ether  is 
so  esoteric,  so  subtilized  from  all  substance,  that  it 
merely  provides  a  nomenclature  for  a  set  of  equations 
expressing  the  propagation  of  radiant  energy.  We 
may  well  go  still  further,  for  I  believe  the  time  is 
rapidly  approaching  when  all  scientific  discussion  of 
the  nature  of  the  ether  will  be  considered  futile. 

In  accordance  with  my  view  no  hypothesis  will  be 
made  to  express  properties  of  a  medium,  whose  exist- 
ence is  itself  incapable  of  scientific  proof.  It  is,  at 
the  same  time,  perfectly  proper  to  distinguish  space 
through  which  we  say  radiant  energy  passes  by  a 
special  name  such  as  the  ether.  The  amount  of 
radiant  energy  in  transit  is  best  given  by  an  equa- 
tion expressing  conservation  of  energy  and  con- 
taining a  velocity  and  an  inertia  factor.  The 
velocity  factor  of  this  equation  most  conveniently 
takes  the  form  of  a  periodic  motion,  but  no  assump- 
tions need  to  be  made  as  to  the  nature  of  the  periodicity 
or  of  the  inertia  factor,  since  they  also  are  not  subject 
to  experimental  verification. 


THE  SCIENTIFIC  METHOD  129 

Such  a  revolution  as  has  occurred  in  the  ideas  of 
the  ether  requires  a  like  one  in  our  ideas  of  matter. 
The  most  notable  effort  in  theoretical  physics,  at  the 
present  time,  is  the  hypothesis  that  the  ultimate  ele- 
ment of  matter  is  not  a  material  atom,  a  sort  of  micro- 
cosm of  sensible  matter,  but  a  free  electrical  charge, 
considered  to  be  an  entity  for  the  purpose;  added  to 
this  are  the  dependent  ideas  that  inertia  and  all  other 
properties  of  matter  are  attributes  of  electricity.  This 
hypothesis  can  mean  nothing  else  than  that  the  Lu- 
cretian  atom,  the  centers  of  force  of  Boscovich,  the 
vortices  of  Kelvin,  and  all  the  atomic  models  (made 
of  weights  and  springs  and  strings),  have  failed  and 
become  useless  as  aids  to  the  imagination. 

Sir  J.  Larmor  defines  this  new  atom  as  a  protion, 
"  in  whole  or  in  part  a  nucleus  of  intrinsic  strain  in 
the  ether,  a  place  at  which  the  continuity  of  the  me- 
dium has  been  broken  and  cemented  together  again  (to 
use  a  crude  but  effective  image)  without  accurately 
fitting  the  parts,  so  that  there  is  a  residual  strain  all 
round  the  place."  This  strain  is  not  of  the  character 
of  mechanical  elasticity,  since  the  "  ultimate  element  of 
material  constitution  is  taken  to  be  an  electric  charge 
or  nucleus  of  permanent  ethereal  strain  instead  of  a 
vortex  ring."  Sir  J.  J.  Thomson  pictures  the  atoms  of 
the  various  chemical  elements  as  nuclei  of  free  positive 
electricity  holding  in  electrical  equilibrium  free  nega- 
tive charges,  placed  in  various  geometrical  designs. 


I3o         THE  LIMITATIONS  OF  SCIENCE 

The  degree  of  stability  of  each  system  is  determined  by 
the  radio-activity  of  its  element.  Professor  Lorentz 
considers  the  protion  to  be  a  small  particle  charged 
with  electricity  and  probably  a  local  modification  of 
the  ether ;  but  his  work  on  electro-magnetic  mass  leads 
one  to  the  opinion  that  he  believes  electricity  to  be  the 
real  essence  of  the  material  universe.  The  modern 
school  of  German  physicists  is  frankly  endeavoring  to 
give  a  purely  electro-magnetic  foundation  to  the 
mechanism  of  the  electron  and  to  mechanical  actions 
in  general. 

Now  to  me,  and  I  believe  to  many  men  of  science,  the 
chief  and  indeed  only  value  of  an  atomic  theory  is  to 
give  a  concrete,  though  crude,  image  of  matter  reduced 
to  its  simplest  conditions.  The  word  electricity  gives 
me  no  such  image  of  matter;  it  conveys  absolutely  no 
idea  of  materiality  nor  even  of  space  or  time  rela- 
tions. What  the  originators  of  the  electrical  atom 
have  done  is  apparently  to  transpose  the  words,  matter 
and  electricity,  tacitly  giving  to  the  latter  all  the  ideas 
usually  associated  with  the  former.  We  may  as  well 
take  the  next  step  at  once  and  raise  the  objective  uni- 
verse on  the  Leibnitzian  monad  or  on  Schopenhauer's 
philosophy  of  "  Die  Welt  als  Wille  und  Vorstellung." 

Again,  the  law  of  the  conservation  of  matter  has 
been  one  of  the  most  fertile  ideas  in  science;  according 
to  this  law  at  least  one  attribute,  inertia,  remains  con- 
stant however  all  others  may  change,  thus  giving  con- 


THE  SCIENTIFIC  METHOD  131 

tinuity  to  material  bodies  as  well  as  to  space  and  time. 
It  is  quite  possible  to  imagine  an  element  of  this  new 
electric  matter  to  be  composed  of  equal  quantities  of 
positive  and  negative  electrons,  whose  motions  are  so 
balanced  as  to  make  all  material  attributes  vanish  and 
produce  a  quasi-annihilation  of  matter. 

Lastly,  when  the  statement  is  made  that  the  electron 
is  merely  a  local  modification  of  the  all-pervading 
ether,  some  idea  should  be  given  us  as  to  the  nature  of 
this  modification.  If  it  is  of  the  character  of  a  strain, 
no  meaning  is  conveyed  unless  this  strain  is  subject  to 
the  laws  of  static  or  kinetic  mechanics.  But  we  have 
no  knowledge  of  a  static  strain  which  fulfils  the  re- 
quirements of  matter,  especially  that  it  must  be  localized 
at  definite  points  and  must  be  uncreatable  and  inde- 
structible; of  kinetic  strains,  the  only  one  at  present 
available  is  the  vortex  ring  of  Helmholtz  and  Kelvin. 
To  imply  that  matter  is  electricity  and  that  electricity  is 
a  static  strain  or  a  vortex  ring,  is  to  make  an  impossible 
assumption  and  is  reasoning  in  a  circle.  If  the  vortex 
ring  of  matter  failed  chiefly  because  Maxwell  said: 
:*  That  at  best  it  was  a  mode  of  motion  and  not  matter 
as  we  know  it,"  what  chance  has  this  new  type  to  sur- 
vive criticism? 

Although  matter  appears  to  us  as  a  continuous  quan- 
tity or  at  least  as  divisible  far  below  our  present 
methods  of  experimentation,  still  it  is  convenient  to 
give  to  the  smallest  observable  portion  of  matter  some 


132        THE  LIMITATIONS  OF  SCIENCE 

such  name  as  protion.  This  unit  of  matter  must  be 
reduced  in  size  as  refinement  of  observation  increases, 
so  that  we  may  always  be  able  to  discuss  it  mathe- 
matically in  the  aggregate  only.  It  must  also  be  en- 
dowed with  the  same  attributes  which  we  recognize  in 
gross  matter. 

At  the  present  time  this  protion  is  the  electron,  and 
the  only  attributes  necessary  to  assign  to  it  are  inertia 
in  the  Newtonian  sense,  a  force  of  gravitational  attrac- 
tion and  a  force  of  electrical  attraction,  either  positive 
or  negative  in  sign.  No  causes  for  these  attributes 
can  be  given,  as  they  are  fundamental.  If  the  experi- 
ments of  Kaufmann,  which  show  that  an  electrified 
particle  in  motion  has  an  apparently  increased  mo- 
mentum, are  cited  as  supporting  the  view  that  inertia 
is  a  function  of  velocity  and  should  be  considered  as 
an  attribute  of  an  invariable  quantity,  the  electrical 
charge,  I  hope  to  show  that  it  is  possible  to  accept 
Kaufmann's  results  and  at  the  same  time  the  invari- 
ability of  inertia.  Before  proceeding  further  with  this 
discussion  it  is  convenient  to  assemble  the  foregoing 
ideas  in  a  more  concise  form. 

We  have  first  postulated  a  real  and  objective  uni- 
verse and  assigned  to  matter  rather  than  to  energy  the 
role  of  being  an  entity.  The  fundamental  attribute  of 
matter  which  makes  it  recognizable  by  our  senses  is 
force. 

We  next  assumed  that  quantitatively  all  phenomena 


THE  SCIENTIFIC  METHOD  133 

may  be  expressed  in  mechanical  ideas  and  that  the 
fundamental  units  of  measurement  are  mass,  length, 
and  time.  These  are  continuous  functions  and  con- 
sequently indefinitely  divisible. 

While  matter,  as  measured  by  mass  and  extent,  is 
indefinitely  divisible,  it  is  convenient  to  adopt  as  a 
scientific  unit  of  mass  a  quantity  so  small  that  it  is 
inferior  to  our  powers  of  observation  and  so  must  be 
treated  mathematically  only  in  aggregates.  As  this  is 
a  general  definition,  the  name  protion  has  been  given 
to  this  unit  in  order  to  avoid  confusion  with  the  chem- 
ical atom  and  the  electron.  At  the  present  time  the 
protion  is  the  electron. 

The  general  laws  governing  actions  are  the  laws  of 
continuity  and  conservation  and  the  law  of  cause  and 
effect.  These  are  generalizations  from  experience  and 
cannot  be  extended  beyond  possible  experience  without 
great  precaution. 

Energy  is  defined  as  the  power  of  doing  work  and  is 
held  to  be  an  attribute  of  matter.  True  or  observa- 
tional energy  is  always  associated  with  matter  and  is 
divided,  for  convenience,  into  potential  and  kinetic 
energy. 

A  third  and  hypothetical  kind  of  energy  is  assumed 
in  order  to  extend  quantitatively  the  laws  of  continuity 
and  conservation,  and  of  cause  and  effect,  to  the 
apparently  well-founded  interchange  of  energy  of 
two  bodies  situated  in  a  vacuum.  This  energy  is  named 


134        THE  LIMITATIONS  OF  SCIENCE 

radiant  energy  and,  in  order  to  link  it  with  kinetic 
energy,  its  quantity  is  expressed  as  the  product  of  a 
"  mass  "  and  a  "  velocity  "  factor.  Its  velocity  is 
naturally  taken  to  be  the  distance  between  the  bodies  di- 
vided by  the  observed  time.  It  is  most  conveniently 
expressed  as  a  periodic  motion  with  a  translational 
velocity  equal  to  3  x  io10  centimeters  per  second.  No 
hypothesis  is  made  in  regard  to  the  nature  of  the  mass 
factor;  it  is  taken  merely  as  a  coefficient  to  maintain 
conservation. 

As  no  attempt  is  made  to  account  for  the  mechanism 
of  radiation,  no  attributes  need  be  assigned  to  an  ether. 
In  fact  no  ether  need  be  postulated,  although  it  is 
advisable  to  use  the  name  to  differentiate  space  when  it 
is  occupied  by  radiant  energy. 

Action  at  a  distance  is  a  matter  of  experience  and 
cannot  be  denied  until  some  reasonable  proof  is  found 
to  account  for  force  by  some  other  means. 

So  far  these  ideas  have  had  the  approval  of  some 
acute  men  of  science,  however  they  may  be  disapproved 
of  by  others.  Those  which  follow  are  more  novel  and 
need  to  be  supported. 

Since  mechanical  explanations  are  to  be  avoided,  it  is 
necessary  to  endow  the  electron  with  all  the  attributes 
of  gross  matter.  For  example,  the  protion  of  oxygen 
has  a  different  density,  force  of  cohesion,  etc.,  from 
that  of  hydrogen.  In  this  discussion,  it  is  necessary 
to  discuss  only  a  few  of  these  attributes. 


THE  SCIENTIFIC  METHOD  135 

I  shall,  therefore,  assume  that  the  electron  has  a 
constant  mass,  mf  and  that  it  possesses  a  force  of  gravi- 
tational attraction  for  all  other  electrons  which  is 
determined  only  by  their  masses  and  the  distance  be- 
tween them. 

The  electron,  in  addition  to  gravitational  attraction, 
has  a  power  of  electrical  attraction.  To  measure  this 
force,  I  shall  assume  that  it  possesses  a  quantity  of 
electricity,  e.  Electrical  force  obeys  the  same  law  as 
gravitational  force,  since  it  is  conditioned  by  the  quan- 
tity of  electricity  and  the  distance  between  electrons. 

The  electrical  property  of  matter  is  also  manifested 
to  us  by  the  experimental  fact,  that  an  electrified  body 
apparently  possesses  a  greater  mass  when  in  motion 
than  an  unelectrified  body.  A  similar  effect  is  noticed 
when  a  body  is  moved  in  a  fluid.  As  the  apparent  in- 
crease in  mass  is  there  due  to  the  resistance  of  the 
medium,  it  is  called  hydrodynamic  mass,  we  may  call 
the  apparent  increase  in  mass  of  a  moving  electron,  its 
electro-magnetic  mass  me.  The  total  or  effective  mass 
is  therefore  m'-f  me. 

Since  the  total  mass  is  found  to  vary  with  the 
velocity  of  an  electron,  two  suppositions  are  possible. 
Most  physicists  now  assume  that  the  mass,  m,  is  a 
variable  and  that  the  mass,  me)  is  constant.  It  seems 
to  me  more  rational  and  more  convenient  to  adopt  the 
converse  idea  that  the  electro-magnetic  mass,  like  the 
hydrodynamic  mass,  is  a  variable.  I  shall,  therefore, 


136        THE  LIMITATIONS  OF  SCIENCE 

assume  that  the  electrical  charge  on  matter  is  a  quan- 
tity varying  with  the  velocity  of  a  body. 

So  great  a  revolution  in  thought  as  to  consider 
inertia  a  variable  quantity  and  to  substitute  electricity 
for  matter  as  the  substance  of  the  universe,  would  only 
have  been  undertaken  from  a  fancied  necessity.  A 
mere  matter  of  convenience  would  scarcely  warrant 
the  labor  of  revising  the  work  of  the  past  and  of  dis- 
carding what  has  been  considered,  until  lately,  as 
definitely  established.  The  need  for  some  such  radical 
change  in  theory  is  based  on  the  experimental  facts  dis- 
covered in  connection  with  the  passage  of  electricity 
through  highly  rarefied  gases,  and  with  radio-activity. 

We  may  consider  it  established  that  the  phenomena 
noted,  when  electricity  is  discharged  in  a  high  vacuum, 
are  most  readily  explained  by  supposing  the  current 
due  to  a  stream  of  electrified  particles  moving  with  a 
velocity  comparable  to  light.  The  experiments  of  Sir 
J.  J.  Thomson  and  C.  T.  R.  Wilson  go  to  show  that 
the  masses  of  these  projectiles,  when  charged  nega- 
tively, are  about  the  one-thousandth  part  of  the  mass 
of  a  hydrogen  atom,  provided  the  charge  on  each  is 
assumed  to  be  the  same  and  equal  to  that  of  the  hydro- 
gen atom.  Those  charged  positively  are  comparable  to 
the  various  chemical  atoms. 

Radio-activity,  on  the  whole,  is  best  explained  by  the 
projection  of  positive  and  negative  electrons  from  a 
certain  class  of  bodies. 


THE  SCIENTIFIC  METHOD  137 

And  lastly,  Kaufmann  has  shown  by  a  delicate  ex- 
periment that  the  apparent  mass  of  an  electron  is  a 
function  of  its  velocity.  This  conclusion  has  been  con- 
firmed by  others,  although  in  minor  points  there  is  a 
considerable  difference  in  results  and  opinions. 

It  must  not  be  lost  sight  of  that  all  these  experiments 
deal  with  quantities  of  matter,  supposing  it  to  exist, 
too  small  to  be  appreciable  by  either  chemical  analysis 
or  mechanical  apparatus,  such  as  the  balance.  They 
are  ultimately  measured  by  the  force  of  electrical  at- 
traction of  an  electrical  charge.  We  are,  therefore, 
experimenting  with  matter  which  appeals  to  us  through 
only  one  of  its  attributes.  Is  it  not  almost  inevitable 
that  an  exclusive  attention  paid  to  this  single  attribute 
is  likely  to  exalt  it  into  an  undue  prominence?  We 
have  had,  in  the  past,  examples  of  much  the  same  sort 
of  reasoning.  When  the  phenomena  of  light  were 
predominantly  discussed,  physicists  drifted  into  the 
opinion  that  this  property  of  matter  could  be  explained 
only  by  creating  a  light  substance.  Again,  this  process 
of  reasoning  occurred  when  heat  was  first  investi- 
gated; we  had  the  creation  of  caloric.  And  now  we 
are  asked  to  do  the  same  thing  with  electricity.  It 
is  safe  to  predict  that  history  will  be  repeated  again, 
and  that  electrical  charges  and  their  forces  will  also 
sink  into  the  condition  of  an  attribute  of  matter. 

It  might  certainly  be  true  that  two  experiments 
showing  equal  electrical  charges  would,  if  we  could 


138        THE  LIMITATIONS  OF  SCIENCE 

measure  the  amount  concerned,  provide  us  with  un- 
equal quantities  of  matter,  just  as  conversely  equal 
quantities  of  matter  might  show  different  quantities 
of  electricity.  The  hypothesis  of  equivalence  of  elec- 
trical charge  and  matter  rests  solely  on  an  analogy  to 
electrolysis,  where  matter  is  in  a  quite  different  state 
and  also  where  the  equivalence  may  be  only  approxi- 
mate. Matter,  on  the  other  hand,  in  a  solid  state  shows 
no  connection  between  volume  and  density  and  elec- 
trical charge.  In  dealing  with  electricity  we  should  not 
forget  the  immense  superiority  of  electrical  detectors 
in  delicacy  to  those  for  mechanical  quantities,  so  that 
we  can  appreciate  far  smaller  quantities  of  electrified 
than  of  neutral  bodies. 

There  is  no  doubt,  from  the  quotations  given,  that 
theorists  are  basing  their  work  on  the  assumption  of 
the  electron  as  the  unit  of  matter.  And  they  give  to  it 
the  following  properties:  Its  mass  is  wholly  electro- 
magnetic; the  motive  forces  are  electric  forces;  and 
the  laws  of  mechanics  are  to  be  deduced  from  the  laws 
of  electro-magnetism. 

At  first  sight,  it  would  seem  to  be  a  simple  matter  to 
devise  an  experiment  which  would  decide  whether  the 
mass  or  the  electrical  charge  of  matter  is  constant. 
But  so  far  these  two  quantities  have  not  only  been 
found  to  be  inseparable  but  they  invariably  enter  as  a 
simple  ratio,  whose  value  decreases  with  increasing 
velocity.  Such  a  relation  can,  of  course,  be  satisfied 


THE  SCIENTIFIC  METHOD  139 

by  assigning  a  proper  variation  either  to  the  numerator 
or  the  denominator.  It  therefore  becomes  a  mere  mat- 
ter of  expedience  which  of  the  two  quantities,  mass  or 
electrical  change,  shall  be  supposed  constant.  In  addi- 
tion, the  quantity,  e/m,  is  itself  a  constant  for  all 
velocities  which  can  be  attained  by  bodies  which  are 
appreciably  large.  So  the  whole  question  of  variation 
is  more  or  less  academic,  in  that  it  does  not  become 
important  unless  we  are  discussing  hypothetical  atomic 
systems. 

To  say  that  e  is  a  constant  is  an  assumption  based 
solely  on  an  analogy  to  the  experimental  laws  of  elec- 
trolysis; but  in  electrolysis,  when  we  obtain  equal 
electrical  charges  we  also  find  equivalent  masses  of 
matter.  In  the  discharge  of  electricity  through  gases 
and  in  radio-activity  the  matter  deposited  is  too  small 
to  be  measured.  This  is  a  fundamental  difference  and 
vitiates  an  analogy  between  the  two.  For  example,  we 
measure  the  amount  of  current  in  a  vacuum  tube  by  an 
electrical  device,  and  at  the  same  time  we  measure  the 
deflection  of  the  current  by  an  electric  and  magnetic 
field;  in  other  words,  all  quantities  and  forces  are 
electrical,  and  we  say  that  equal  currents  in  this  case 
require  equivalent  quantities  of  matter.  But  it  has 
not  been  shown  to  be  impossible  or  even  improbable 
that  electrons,  associated  with  equal  quantities  of  mat- 
ter but  having  different  velocities,  might  show  different 
electrical  charges;  or  that  electrons  producing  equal 


I4o         THE  LIMITATIONS  OF  SCIENCE 

electrical  charges,  might  deposit  different  amounts  of 
matter  if  it  were  sufficient  in  quantity  to  be  detected  by 
chemical  or  mechanical  reactions. 

As  an  hypothesis,  I  propose  that,  in  order  to  make 
the  ratio  ~  agree  with  the  experimental  evidence  of  its 
value  and  to  account  for  electro-magnetic  mass,  we 
consider  m  to  be  the  mass  of  a  particle  of  matter  in 
the  Newtonian  sense,  of  constant  and  small  value,  and 
e,  the  electrical  charge,  to  be  a  force  attribute  of  mat- 
ter which  varies  with  the  velocity  of  the  particle. 

However  novel  this  hypothesis  may  be,  I  have  not 
been  able  to  find  any  experimental  facts  more  difficult 
to  explain  by  it  than  by  any  of  the  other  hypotheses 
which  have  been  recently  advanced ;  and,  on  the  other 
hand,  it  apparently  accounts  for  much  of  the  modern 
work  in  terms  of  old  and  well-established  ideas. 

From  the  very  nature  of  my  conception  of  the  limits 
which  should  be  imposed  on  scientific  inquiry,  I  make 
no  attempt  to  explain  the  cause  for  this  electrical  prop- 
erty of  matter  any  more  than  I  should  for  its  gravita- 
tional attributes.  Both  are  fundamental  phenomena  to 
be  accepted  as  experimental  facts  until  we  gain  con- 
trary knowledge.  Indeed,  I  have  ventured  to  indulge 
in  this  speculation  rather  with  the  idea  of  showing 
that  the  recent  hypotheses  for  electricity  and  matter; 
for  the  ether,  protions,  and  corpuscular  light;  for  the 
electro-magnetic  and  other  non-Newtonian  mechanics, 
are  not  necessary.  We  may  still  account  as  adequately 


THE  SCIENTIFIC  METHOD  141 

for  all  our  experimental  facts  by  a  simple  addition  to 
the  attributes  of  matter  and  continue  to  base  our 
theories  on  mechanical  laws. 

So  long  as  the  measurement  of  physical  qualities  be- 
comes ultimately  a  matter  of  measuring  mechanical 
forces,  it  is  advisable  to  express  quantitative  physical 
laws  in  terms  of  mechanical  formulae.  For  this  rea- 
son electricity  should  be  considered  a  function  of  me- 
chanical energy  rather  than  the  converse.  If  it  be 
possible  to  place  mechanics  on  an  electro-dynamic  basis, 
it  is  certain  that  we  may  always  explain  electricity  in 
terms  of  pondero-dynamic  laws.  As  both  are  possible, 
it  seems  far  more  natural  and  more  rational  to  con- 
sider electricity  as  an  attribute  of  matter  than  matter 
as  a  phenomenon  of  electricity. 


CHAPTER  V 

THE  CLASSICAL  AND  THE  NEW 
MECHANICS 

Mathematica,  quae  philosophiam  naturalem  terminate,  non 
generate  aut  procreare. — BACON. 

So  far  the  hypothetical  method  has  been  discussed 
in  its  broader  aspects.  It  is  my  purpose  now  to  out- 
line its  effect  on  science  and  on  men  of  science  by  con- 
sidering certain  special  cases.  I  know  of  no  better 
way  to  point  out  the  influence  of  this  method  on  sci- 
ence than  to  contrast  the  classical  mechanics,  founded 
on  the  work  of  Galileo,  Descartes,  and  Newton,  and 
developed  in  accordance  with  the  abstractive  or  real- 
istic method,  with  the  new  mechanics  which  is  based 
on  electricity  as  a  substance  and  on  electro-dynamic 
energy,  and  which  is  pronouncedly  speculative  in  char- 
acter. 

All  phenomena  of  a  mechanical  nature  can  be  re- 
duced ultimately  to  modifications  of  inertia,  velocity, 
momentum,  and  energy.  Theories  of  mechanical  ac- 
tion have,  in  addition,  this  common  property;  they 
begin  with  the  postulate  of  an  entity  which  possesses 

inertia  and  velocity.     Various  names  have  been  at- 

142 


CLASSICAL  AND  NEW  MECHANICS      143 

tached  to  this  entity,  but  whether  it  be  called  an  atom, 
an  ether,  a  vortex,  electricity,  or  energy,  its  function 
is  the  same.  While  there  is  little  difference  in  the 
nature  of  this  entity  or  substance,  yet  there  are  two 
diametrically  opposite  ways  of  considering  its  space 
attributes  which  give  rise  to  two  irreconcilable  schools 
of  thought.  One  of  these  considers  the  primordial  sub- 
stance to  be  discontinuous  with  its  parts  separated  by 
vacuous  spaces,  and  the  other  school  just  as  con- 
fidently assumes  that  there  can  be  no  empty  spaces, 
and  that  all  space  is  therefore  continuous.  Arguments 
for  and  against  these  two  views  have  been  unceasing 
and  are  likely  to  continue,  so  long  as  hypothetical 
methods  remain  in  vogue.  The  problem  is  quite  in- 
capable of  solution  because  the  postulate  of  continuity 
or  discontinuity  is  a  matter  of  conviction  rather  than 
of  reason.  The  fact  is,  we  believe  one  or  the  other  to 
be  true  and  that  is  the  end  of  it.  In  such  discussions 
where  a  postulate  is  beyond  our  powers  of  verifica- 
tion by  experience,  each  contestant  chooses  his  starting- 
point,  and  this  once  chosen,  his  argument  in  favor  of 
it  is  as  sound  as  that  of  his  opponents.  And  the  truth 
of  this  assertion  is  evident,  because  from  these  dia- 
metrically opposite  postulates,  conclusions  which  are 
quite  identical  are  deduced  by  equally  logical  argu- 
ments; witness  the  controversy  between  the  atomists 
and  the  Cartesians  which  see-saws  through  all  scientific 
theory  and  is  as  far  from  settlement  to-day  as  it  was 


144         THE  LIMITATIONS  OF  SCIENCE 

centuries  ago.  This  dualism,  as  it  may  be  called, 
is  not  confined  to  science;  it  is  but  one  phase  of  that 
larger  dualism  of  philosophy  and  ethics  which  has 
come  down  to  us  from  the  Greek  thinkers ;  the  claims 
of  two  opposing  schools  of  thought  are  always  present 
to  show  us  that,  if  the  mind  can  develop  a  system  from 
one  set  of  postulates,  the  same  results  can  be  obtained 
from  their  contraries. 

If  then  our  conception  of  the  nature  of  things  is 
but  a  matter  of  personal  conviction,  what  value  is 
there  in  the  opinion  of  Professor  Lorentz,  which  I 
have  already  quoted, — if  we  wish  to  obtain  an  in- 
sight into  the  mysteries  and  operations  of  nature,  we 
must  make  hypotheses?  If  such  hypotheses  are  not 
capable  of  proof  then  they  must  rest  on  what  Boling- 
broke  so  aptly  calls  our  inward  sentiment  of  knowl- 
edge. The  experimentalist  who  described  phenomena 
from  his  inward  sentiment  of  what  they  should  be 
rather  than  from  observations  of  what  they  are,  would 
be  classed  as  a  nuisance.  Such  a  one  not  only  does  not 
advance  our  knowledge  but  he  actually  retards  it,  since 
his  work  must  be  repeated  before  the  truth  can  be 
known.  So,  too,  the  theorist,  who  relies  on  his  per- 
sonal conviction  and  not  on  facts  and  laws,  builds  a 
structure  which  is  not  only  temporary  and  false  but 
must  be  torn  down.  If  we  relegate  to  metaphysics  so 
large  a  part  of  what  is  commonly  called  physics,  what 
is  left  to  the  science  of  physics?  The  answer  probably 


CLASSICAL  AND  NEW  MECHANICS      145 

is  to  be  found  in  the  saying  of  Lord  Kelvin,  that  no 
scientific  statement  is  understood  until  it  is  measured. 
If  we  grant  this,  then  we  must  first  examine,  in  such 
a  discussion  as  this,  our  methods  of  measurement. 

The  statement  of  a  phenomenon  invariably  contains 
two  terms,  called  qualitative  and  quantitative  factors; 
the  former  expressing  "  what  kind  "  and  the  latter, 
"  how  much."  Thus,  when  we  speak  of  a  distance  as 
ten  centimeters,  we  mean  that  we  are  to  consider  a 
quantity,  ten,  of  the  quality,  length.  Now  it  is  not 
really  the  province  of  science  to  seek  for  absolute 
knowledge  of  either  qualities  or  quantities,  and  the 
attempt  to  do  so  is  the  excuse  for  hypothesis.  What 
science  is  concerned  with  is  the  relative  knowledge,  or 
comparison,  of  different  quantities  of  any  quality  and 
the  reduction  of  complex  qualities  into  combinations 
of  simpler  ones. 

It  thus  becomes  of  prime  importance  to  settle  on  the 
simplest  and  most  fundamental  qualities  which  may 
serve  as  a  foundation  for  our  system  of  measurement. 
Because  of  the  fact  that  mechanical  motions  and  me- 
chanical forces  are  the  most  readily  perceived  by  us 
and  are  most  easily  expressed  in  mathematical  for- 
mulae, the  fundamental  units  of  quality  are  always 
selected  from  mechanical  concepts.  Of  these,  length, 
time,  and  mass  or  inertia,  are  found  to  be  incapable 
of  further  simplification  and  have  been  adopted  as  the 
units  of  measurement.  As  these  qualities  must  enter 


146         THE  LIMITATIONS  OF  SCIENCE 

into  all  equations  quantitatively  and  as  we  can  have 
no  conception  of  an  absolute  quantity,  we  have  by 
statute  fixed  upon  certain  arbitrary  standards  of  quan- 
tity, such  as  the  centimeter  and  foot  for  length,  the 
gramme  and  pound  for  mass,  and  the  second  for  time. 
From  these  prime  standards,  all  other  quantities  of  a 
mechanical  nature  may  be  readily  derived,  as  for  ex- 
ample :  velocity  is  the  quotient  of  a  given  length  by  a 
time;  momentum  is  the  product  of  a  mass  and  a 
velocity;  energy,  one-half  the  product  of  a  mass  and  a 
square  of  a  velocity,  etc. 

As  I  have  already  pointed  out,  the  science  of  me- 
chanics is  the  only  branch  of  physics  which  has  a 
completely  developed  theory.  Not  only  is  this  the  case, 
but  the  other  branches  of  physics  have  been  developed 
from  a  mechanical  basis,  in  so  far  at  least  as  the  meas- 
urement of  all  phenomena  is  now  made  in  terms  of 
these  mechanical  units.  This  coordination  in  physics 
has  the  great  advantage  of  making  it  possible  to  express 
what  are  apparently  unrelated  phenomena  by  using 
combinations  of  only  three  standards  of  measurement 
and  by  a  few  general  equations  of  mechanics.  And 
we  attain  the  additional  advantage  of  expressing  all 
these  phenomena  in  the  most  concrete  form  imagi- 
nable. But,  on  the  other  hand,  this  method  produces 
a  serious  break  between  physics  and  certain  other  sci- 
ences, especially  those  which  rely  more  exclusively  on 
the  sense  perceptions  as  criteria  for  classification  of 


CLASSICAL  AND  NEW  MECHANICS      147 

phenomena.  Thus,  to  the  physicist  light  of  different 
kinds  is  distinguished  only  by  the  three  qualities  pos- 
sible in  a  mechanical  wave;  its  wave-length,  the 
amplitude  of  its  disturbance,  and  the  complexity  of  its 
form.  These  same  qualities  must  also  serve  to  dis- 
tinguish sounds,  water  waves,  and  many  other  types  of 
this  kind  of  motion.  For  the  biologist  and  psychol- 
ogist, light  is  distinguished  by  its  tint,  intensity,  and 
saturation,  the  three  qualities  which  affect  the  sense  of 
sight,  and  sound  is  determined  by  pitch,  loudness,  and 
timbre,  which  affect  the  auditory  nerve.  And  as  there 
is  no  relation  between  the  sensations  of  sight  and  hear- 
ing, so  there  can  be  no  connection  between  light  and 
sound.  While  the  method  of  the  physicist  has  the 
great  advantage  of  unity,  yet  it  suffers  from  its  arti- 
ficiality, as  it  tends  to  bring  into  undue  prominence  the 
mechanical  energy  involved  in  producing  light  and 
sound  and  ignores  the  more  important  property  of 
these  phenomena:  their  effect  on  our  senses. 

It  is  generally  conceded  that  we  have  no  abstract  or 
absolute  knowledge  of  a  quantity  of  length,  time,  or 
mass.  In  other  words,  we  can  express  any  of  these 
three  quantities  only  as  a  numerical  ratio  with  respect 
to  a  predetermined  standard  of  the  same  quantity,  such 
as  a  yardstick  for  length,  a  pound  for  mass,  and  a 
given  motion  of  a  clock-hand  or  of  the  rotation  of 
the  earth  for  time.  And,  from  this  fact,  it  is  often 
argued  that  we  cannot  form  any  idea  of  the  qualities, 


148        THE  LIMITATIONS  OF  SCIENCE 

space,  time,  and  matter,  except  as  they  are  individually 
and  concretely  measured.  Kant,  to  be  sure,  main- 
tained that  we  were  endowed  with  an  innate  and  inex- 
plicable, but  sufficient  idea  of  pure  space  and  time. 
These  qualities  are,  however,  by  themselves  inappreci- 
able to  our  senses.  To  make  them  sensible,  we  need 
a  third,  which  he  calls  the  Ding  an  sich,  corresponding 
in  the  external  world  to  what  we  call  the  entity, 
matter. 

However  vulnerable  and  unsatisfactory  the  doctrine 
of  innate  ideas  may  be,  yet  it  seems  to  me  that  by  the 
abstractive  method  as  used  in  the  science  of  mechanics 
we  do  obtain  a  real  and  adequate  idea  of  these  three 
fundamental  postulates.  If  we  have  not  such  a  power 
of  abstracting  real  ideas  from  our  concrete  observa- 
tions of  phenomena,  then  it  is  difficult  to  believe  that 
the  conclusions  of  Euclidean  geometry  and  of  mathe- 
matical analysis  in  general  are  rigorous.  Thus,  in 
mathematical  definitions,  space  is  a  mere  volume  en- 
closed in  an  imagined  boundary  which  may  be  con- 
ceived as  of  any  extent  from  the  indefinitely  small  to 
the  indefinitely  large.  And  this  imagined  bounding 
surface  bears  no  closer  relation  to  a  concrete  material 
envelope  than  does  an  image  in  a  mirror  to  its  object. 
It  seems  to  me  that  I  have  an  adequate  idea,  for 
instance,  of  the  space  in  an  empty  room  and  that  I 
can  abstract  all  the  properties  from  my  concrete  per- 
ception of  the  material  walls  of  this  room  except  the 


CLASSICAL  AND  NEW  MECHANICS      149 

one  fact  that  they  inclose  this  space.  By  deduction 
and  by  experience  I  am  convinced  that  this  space  is 
not  empty,  but  contains  air.  But  it  is  really  more 
difficult  to  appreciate  the  existence  of  the  air,  if  it  be 
at  rest,  than  its  non-existence.  This  belief  is  borne 
out  by  the  slow  advance  in  the  conception  of  the  exist- 
ence of  gases.  And  it  also  seems  true  to  me  that  I 
have  an  adequate  idea  of  an  area  inclosed  in  a  tri- 
angle, because  I  can  think  of  the  area  inclosed  by  three 
abstract  lines  and  refrain  from  thinking  of  the  con- 
crete volume  of  any  real  lines  drawn  with  a  pencil. 

As  for  the  concept  time,  we  have  a  twofold  sense 
of  it;  one  is  the  coincidence  of  an  event  with  the  posi- 
tion of  the  hands  of  a  clock  or  of  the  earth.  But  we 
have,  in  addition,  a  much  more  general  idea  of  time, 
as  mere  succession  of  events  without  any  reference  to 
such  a  standard  of  measurement  as  the  second  or 
minute.  This  might  be  called  our  belief  that  events 
entirely  unconnected  with  our  own  experience  occur 
successively  just  as  those  events  do  which  we  com- 
pare with  a  clock.  We  have,  on  awaking  from  sleep, 
a  distinct  and  clear  idea  that  events  have  transpired 
successively  during  our  unconsciousness  and  without 
any  reference  to  a  measured  interval  of  time.  This 
general  knowledge  of  "  before  and  after  "  is  appa- 
rently possible  to  an  animal ;  a  dog  will  with  certainty 
expect  a  reward  after  the  performance  of  a  trick  and 
not  before  or  during  it. 


150        THE  LIMITATIONS  OF  SCIENCE 

As  for  the  third  postulate,  which  is  called  matter,  it 
may  be  taken  in  the  most  general  sense  as  the  some- 
thing which  makes  space  and  time  concrete  or  sensible. 
The  necessity  in  science  for  such  a  postulate  is  clear, 
for  science  deals  with  the  phenomena  of  an  objective 
world.  Even  those  men  of  science  most  opposed  to 
the  idea  that  mass  is  the  measure  of  matter  still 
postulate  an  entity  identical  with  matter,  as  just  de- 
fined, although  they  may  call  it  by  a  different  name, 
such  as  energy  or  electricity.  And  the  distinction  be- 
tween mathematics  and  science  lies  in  the  conception  of 
this  third  postulate.  In  pure  mathematics,  matter  be- 
comes the  abstract  postulate,  quantity.  When  discuss- 
ing velocity  abstractly  there  is  then  no  need  to  con- 
sider the  properties  of  the  thing  moving,  but  in  physics 
there  is  such  a  need.  Or  again,  when  dealing  with 
space  relations  the  mathematician  is  in  no  way  limited 
to  the  restricted  number  of  three  dimensions  which  our 
sense  perception  of  the  material  universe  imposes  on 
science. 

The  supreme  value  of  mathematics  to  science  is  due 
to  the  fact  that  scientific  laws  and  theories  have  their 
best,  if  not  their  only  complete,  expression  in  mathe- 
matical formulae;  and  the  degree  of  accuracy  with 
which  we  can  express  scientific  theory  in  mathematical 
terms  is  a  measure  of  the  state  of  a  science.  Thus 
it  is  possible  to  classify  sciences  according  to  their 
development,  from  the  accumulation  of  statistics  of 


CLASSICAL  AND  NEW  MECHANICS      151 

phenomena  to  the  generalization  of  these  phenomena  in 
comprehensive  and  rigorous  laws.  In  such  a  classi- 
fication, sociology  or  the  study  of  existing  society  oc- 
cupies the  lowest  rank,  since  true  laws  can  be  derived 
only  from  actions  whose  completed  consequences  are 
known.  Sociology  therefore  attempts  to  found  its 
laws  on  the  data  of  history,  the  study  of  past  society; 
history  must  in  the  same  way  rely  on  psychology, 
which  deals  with  the  actions  of  the  individuals  of 
society;  psychology  relies  on  biology;  biology,  on 
chemistry;  chemistry,  on  physics;  and  physics,  on  pure 
mathematics.  While  each  science  thus  strives  to  found 
its  laws  on  the  conclusions  of  the  following  science, 
each  succeeds  only  partially;  this  leads  us  to  a  paradox. 
The  goal  of  science  is  mathematics,  and  while  mathe- 
matics may  be  said  to  be  the  only  true  science  since  it 
has  the  only  true  scientific  method,  mathematics  is  not 
a  science  because  it  deals  with  abstractions  and  ignores 
concrete  phenomena. 

As  stated  before,  all  quantities  in  mechanics  may 
be  expressed  by  combining  the  fundamental  units, 
length,  mass,  and  time,  in  simple  ratios  and  products. 
And,  while  the  phenomena  of  light,  heat,  and  elec- 
tricity do  not  manifest  themselves  qualitatively  to 
our  senses  in  any  manner  which  may  be  coordinated 
with  mechanical  actions,  yet  we  endeavor  to  measure 
them  quantitatively  in  physics  as  if  they  were  wholly 
mechanical  in  nature.  Thus  we  speak  of  the  velocity 


152        THE  LIMITATIONS  OF  SCIENCE 

of  light  from  the  sun  to  the  earth,  as  if  we  were 
considering  a  real  mechanical  motion  of  a  ponderable 
body,  although  in  the  intervening  space  there  is  no 
matter.  The  only  thing  we  have  been  able  to  observe 
is,  that  light  emitted  from  the  sun  appears  on  the  earth 
some  time  later.  Light,  as  a  phenomenon,  does  not 
exist  unless  it  is  associated  with  matter;  we  can  no 
more  discuss  the  amount  of  light  or  its  velocity  in 
vacuous  space  than  we  can  speak  of  the  temperature 
of  such  space.  Light  has  a  true  mechanical  velocity 
when  passing  through  space  occupied  by  matter,  for 
then  we  can  observe  and  measure  its  path  as  well  as 
the  time  function  and  so  obtain  a  value  for  velocity. 
From  observations  on  the  velocity  of  light  in  matter 
and  from  analogy  to  the  phenomena  of  sound  trans- 
mission, which  takes  place  only  in  spaces  occupied  by 
matter,  we  by  the  hypothetical  method  transfer  the 
measurements  and  laws  of  light  in  transparent  bodies 
to  space  not  occupied  by  matter.  The  very  assump- 
tion of  a  light  velocity  in  immaterial  spaces  requires 
us  also  tacitly  to  assume  that  something,  in  a  mechan- 
ical sense,  is  moving.  Once  we  have  granted  that  light 
is  something  moving,  then  all  the  other  phenomena  of 
light  permit  of  a  hypothetical  mechanical  explanation, 
and  we  have  the  right  to  speak  of  the  momentum  and 
energy  of  this  light  something,  whether  it  be  corpuscles 
or  waves.  But  it  is  the  easiest  thing  in  the  world  to 
forget  that  we  can  never  obtain  any  real  knowledge 


CLASSICAL  AND  NEW  MECHANICS      153 

of  this  something  we  have  called  light.  It  is  sur- 
prising that  men  of  science  should  believe  that  they 
have  proved  the  existence  of  the  ether,  as  when  Sir 
Oliver  Lodge  states  that  it  is  the  most  massive  thing 
imaginable;  or  that  space  is  occupied  by  energy,  an 
entity  possessing  inertia  and  probably  gravitational 
force,  as  Professor  Einstein  announces:  they  should 
see  that  such  statements  are  not  deductions  made  from 
our  experimental  knowledge  of  light,  but  are  already 
contained  in  the  postulate  that  light  is  mechanical  and 
has  a  mechanical  velocity. 

It  is  instructive  to  consider,  in  this  connection,  how 
we  also  have  attached  hypothetically  the  science  of 
electricity  to  mechanics.  The  fundamental  phenome- 
non observed,  when  bodies  are  electrified  or  magnet- 
ized, is  that  they  attract  or  repel  each  other  with  a 
mechanical  force  which,  like  the  force  of  gravitation, 
varies  inversely  as  the  square  of  the  distance  between 
them.  In  our  fundamental  units  this  mechanical  force 
is  equal  to  a  mass  times  a  length  and  divided  by  the 
square  of  a  time.  Now  Coulomb,  who  discovered 
and  measured  the  law  of  electrical  attraction,  believed 
that  electricity  was  a  kind  of  fluid  substance,  such  as 
was  always  introduced  when  phenomena  were  obscure ; 
and  with  this  idea  in  his  mind,  he  employed  the  term 
quantity  of  electricity  to  indicate  an  analogy  with  a 
quantity  of  matter.  On  this  supposition,  a  quantity 
of  electricity  expressed  in  mechanical  units  is  equal  to 


154        THE  LIMITATIONS  OF  SCIENCE 

the  square  root  of  a  length  times  a  mass.  Now  it  is 
quite  certain  that  a  quantity  of  electricity  has  nothing 
in  common  with  length.  Taking  a  step  further,  we 
find  that  the  resistance  of  a  conductor  to  an  electrical 
current  may  be  expressed  as  a  velocity.  Yet  it  would 
be  absurd  to  attach  any  concrete  relation  between  elec- 
trical resistance  and  mechanical  velocity. 

These  three  examples  of  velocity  illustrate  quite 
clearly  the  difference  between  the  abstractive  and  hypo- 
thetical methods.  From  the  definite  and  clear  idea  of 
the  mechanical  velocity  of  a  concrete  body,  we  pass  to 
an  indefinite  idea  of  the  velocity  of  light  in  empty 
space  and  in  order  to  link  this  idea  to  mechanical 
notions,  we  assign  to  light  a  hypothetical  material 
existence.  But  our  mathematical  equations  lead  us  a 
step  further  and  we  can  derive  a  purely  formular  rela- 
tion between  mechanical  velocity  and  electrical  resist- 
ance; in  this  case  analogy  between  physics  and  mathe- 
matics entirely  fails  and  no  idea,  even  hypothetical, 
has  been  attached  to  the  result. 

The  principles  of  the  science  of  mechanics,  on  which 
the  theories  of  the  other  branches  have  been  built, 
date  from  the  time  of  Galileo  and  Newton.  As  they 
had  withstood  the  searching  criticism  of  the  masters 
of  the  science  for  centuries  without  having  been  shown 
to  be  either  false  or  inadequate,  the  belief  grew  that 
however  other  theories  of  physics  might  change,  the 
laws  of  mechanics  as  stated  by  Newton  were  prob- 


CLASSICAL  AND  NEW  MECHANICS      155 

ably  final.  But  it  is  inevitable  that  if  we  found  the 
laws  of  light  and  electricity  on  mechanics,  the  time  will 
come  when  the  accumulation  of  knowledge  will  in- 
crease the  discrepancies  which  must  always  exist  be- 
tween any  two  branches  of  science  and  which  will 
eventually  require  a  thorough  revision  of  one  or  the 
other.  If  the  attention  be  directed  more  toward  dis- 
covering the  phenomena  and  laws  of  light  and  elec- 
tricity than  of  mechanics,  as  it  is  to-day,  these 
discrepancies  will  probably  be  laid  to  the  laws  of 
mechanics  and  their  revision  will  be  attempted  to 
insure  agreement.  This  has  occurred  in  the  last  few 
years,  and  the  mechanics  based  on  material  bodies  is 
being  replaced  by  a  mechanics  of  electricity  or  by  one 
of  energy,  if  the  terms  be  permissible. 

The  mechanics  of  material  bodies,  to  which  the  name 
of  Newton  is  generally  attached,  was  based  on  the  ob- 
jective reality  of  matter,  whose  quantitative  measure 
was  inertia  or  mass.  Newton  evidently  considered 
inertia  as  a  fundamental  attribute  of  matter,  and  thus 
invariable  and  inexplicable;  something  to  be  accepted 
and  determined  solely  by  experiment.  Thus  he  says 
in  his  Principia:  "  Haec  (materiae  vis)  semper  pro- 
portionalis  est  suo  corpori,  neque  differt  quicquam  ab 
inertia  massae,  nisi  in  modo  concipiendi.  Per  inertiam 
materiae  fit,  ut  corpus  omne  de  statu  suo  vel  quiescendi 
vel  movendi  difficulter  deterbetur."  This  postulate  may 
•be  freely  translated  to  mean  that  the  force  of  attrac- 


156         THE  LIMITATIONS  OF  SCIENCE 

tion  of  matter  is  always  proportional  to  the  amount  of 
matter  acting,  and  does  not  differ  in  any  way  from  the 
inertia  of  mass  except  in  our  method  of  apprehending 
it.  By  inertia  of  matter  is  meant,  that  a  body  can  be 
changed  from  its  previous  condition  of  rest  or  motion 
only  by  this  material  force.  It  is  evident  that  he 
regarded  inertia  as  an  inherent  and  inalienable  prop- 
erty of  a  body,  independent  of  the  influence  of  any 
other  body  or  ether,  and  forming  the  connecting  link 
between  ourselves  and  the  external  world.  Such  being 
the  case,  how  may  we  decide  what  is  the  mass  of  any 
particular  body?  If  a  number  of  individuals  measure 
experimentally  a  mass,  or  even  if  one  of  them  measures 
it  several  times,  no  two  observations  will  agree.  Which 
observation  gives  the  correct  value?  Newton  would 
have  answered,  none  of  them.  Data  of  objective  phe- 
nomena can  never  be  known  exactly ;  each  value  we  ob- 
tain approximates  to  the  truth,  and  the  approximation 
is  the  closer,  the  greater  the  number  so  obtained  and 
the  greater  the  care  exercised.  The  final  result  must 
be  deduced  from  all  the  observations,  according  to  a 
well  developed  mathematical  theory  of  errors.  The 
same  reasoning  was  held  to  apply  to  observations  on 
the  space  dimensions  of  a  body  and  on  the  time  occur- 
ring during  any  event. 

While  the  idea  was  advanced  in  this  mechanics  that 
the  position  and  motion  of  any  body  could  be  deter- 
mined only  from  the  position  of  some  other  body, 


CLASSICAL  AND  NEW  MECHANICS      157 

supposed  for  the  time  being  to  be  at  rest,  or  that  posi- 
tion and  motion  were  relative  and  not  absolute;  yet  it 
was  not  explicitly  stated  that  there  could  not  be  absolute 
rest  or  motion,  such  as  would  occur  if  the  motion  of  a 
body  were  referred  to  an  absolutely  fixed  center  of  the 
universe  or  to  an  ether  which  was  incapable  of  motion. 
For  all  practical  problems,  Newton's  third  law  of  mo- 
tion, which  states  that  to  every  action  there  is  an 
equal  and  oppositely  directed  reaction,  announces  the 
universality  of  relativity. 

We  should  finally  note,  that  mass,  dimensions,  and 
time  were  held  to  be  unaffected  by  the  motion  of  a 
body.  Newton  expresses  this  by  saying  that  force 
actions  of  matter,  or  the  science  of  dynamics,  are  inde- 
pendent of  its  initial  state  of  rest  or  motion. 

The  first  serious  criticism  of  these  postulates  was 
made  by  a  number  of  physicists,  forming  what  is  often 
called  the  school  of  energetics,  who  proposed  to  sub- 
stitute energy  for  mass  as  the  fundamental  attribute 
of  matter.  At  the  time,  the  change  was  rather  imma- 
terial as  we  were  accustomed  to  think  that  mass  and 
energy  were  coexistent  and  that  either  one  was  unin- 
telligible without  the  other.  As  I  have  said  before,  it 
was  the  same  kind  of  a  problem  as  deciding  which  came 
first,  the  owl  or  the  egg;  the  answer  to  which  is  we 
know  nothing  about  the  matter. 

The  discrepancies  between  electricity  and  mechanics 
did  not  prove  to  be  embarrassing  until  certain  problems 


158        THE  LIMITATIONS  OF  SCIENCE 

connected  with  light  and  electricity  became  pressing. 
Of  these,  three  stand  out  most  prominently. 

The  phenomena  associated  with  electricity  when  it 
passes  through  very  high  vacua  and  with  radio-active 
bodies  like  radium  are  now  explained  as  being  due  to 
the  action  of  excessively  small  particles,  carrying  a 
charge  of  electricity  and  moving  with  a  velocity  com- 
parable to  the  velocity  of  light,  or  about  one  hundred 
thousand  miles  per  second.  These  particles,  both  be- 
cause of  their  smallness  and  because  of  their  velocity, 
are  in  an  entirely  different  class  from  the  bodies 
previously  considered  in  mechanics  which  have  a  sen- 
sible mass  and  whose  greatest  velocity  is  less  than  one 
hundred  miles  per  second.  Errors  in  mechanical  laws 
which  would  otherwise  be  inappreciable  may  easily 
assume  large  proportions  when  applied  to  such  ex- 
treme cases.  The  hypothesis  of  the  electron  has 
profoundly  modified  the  conception  of  the  atom,  and 
the  nature  of  matter  and  motion. 

In  the  second  place,  recent  experiments  lead  to  the 
belief  that  matter  is  always  electrified;  that  light  is 
due  to  electrical  variations;  and  that  the  amount  of 
electricity  associated  with  a  given  amount  of  matter  is 
a  fixed  and  invariable  quantity.  It  is  further  shown 
by  theory  and  confirmed  by  experiment  that  if  an 
electrified  body  be  moved,  the  ratio  of  its  electrical 
charge  to  its  apparent  mass  must  vary  with  the  velocity 
of  its  motion;  and  since  the  electrical  charge  is  assumed 


CLASSICAL  AND  NEW  MECHANICS      159 

to  be  a  constant,  there  remains  only  the  alternative  of 
considering  the  mass  of  a  body  as  a  variable.  This 
evidently  strikes  at  the  very  root  of  Newtonian  me- 
chanics. The  effect  of  motion  on  mass  is  found  to  be 
inappreciable  until  the  velocity  approximates  to  that  of 
light,  so  the  discussion  would  have  remained  a  purely 
academic  one,  if  the  creation  of  the  electron  had  not 
brought  us  suddenly  face  to  face  with  bodies  which 
are  supposed  to  have  a  velocity  great  enough  to  affect 
experimentally  their  mass.  A  further  consequence  of 
this  theory  is  that  mass  becomes  infinite  when  the 
velocity  of  light  is  reached.  While  that  velocity  has 
always  been  considered  enormous  and  beyond  our 
power  to  attain,  such  a  result  was  entirely  unsuspected. 
The  laws  of  mechanics  of  bodies  at  rest  could  evidently 
no  longer  be  held  to  be  the  same  as  those  for  bodies  in 
motion. 

Lastly,  various  experiments  have  been  made  to  find 
an  effect  due  to  the  mutual  relations  of  the  ether  and 
matter.  None  could  be  found.  One  in  particular,  de- 
vised by  Professors  Michelson  and  Morley,  has  proved 
to  be  the  hardest  problem  in  modern  physics  to  explain. 
Calculation  showed  that  certain  properties  of  light 
which  depend  on  its  velocity  should  be  affected  appre- 
ciably by  the  motion  of  the  earth  through  space,  but 
the  experiment  proved  beyond  doubt  that  such  was  not 
the  case.  The  first  attempt  at  a  reconciliation  was 
made  by  assigning  certain  complicated  motions  to  the 


160        THE  LIMITATIONS  OF  SCIENCE 

ether  which  would  annul  the  effect  the  motion  of  the 
earth  should  produce;  but  it  was  shown  that  unless  the 
ether  remains  absolutely  at  rest  worse  difficulties  re- 
sult. Then  the  bold  assumption  was  made,  often 
called  the  Fitzgerald-Lorentz  effect,  that  the  dimen- 
sions of  bodies  in  motion  were  so  changed  by  their 
motion  as  to  neutralize  the  effect  of  the  earth's  motion 
on  the  phenomena  of  light.  Every  body  would,  accord- 
ing to  this  idea,  grow  shorter,  the  faster  it  moved; 
and  would  flatten  out  to  a  disc  of  no  thickness  if  it 
could  attain  a  speed  equal  to  the  velocity  of  light. 

One  of  the  results  of  this  criticism  of  mechanics  has 
been  to  change  profoundly  our  hypothesis  of  the  ether. 
As  is  well  known,  the  early  conception  of  the  ether  was 
a  kind  of  material  substance  possessing  properties  in- 
compatible with  those  of  any  other  kind  of  matter.  A 
large  part  of  the  effort  of  theorists  down  to  the  middle 
of  the  nineteenth  century  was  devoted  to  inventing 
attributes  for  it  which  would  enable  it  to  fulfill  its  func- 
tion as  the  medium  for  the  transmission  of  light.  At 
this  time,  Faraday  discovered  an  effect  in  electricity 
which  required  an  entire  change  in  our  ideas  of  the 
ether.  When  he  found  that  static  electric  charges  and 
forces  were  dependent  on  the  characteristics  of  the 
material  substance  in  which  electrified  bodies  were  im- 
mersed, and  when  later  Maxwell  predicted  and  Hertz 
showed  experimentally  that  electro-magnetic  energy 
passed  through  vacuous  space,  and  that  this  form  of 


CLASSICAL  AND  NEW  MECHANICS      161 

radiant  energy  was  undoubtedly  of  the  same  type  as 
light  and  heat;  then  it  was  found  that  no  material 
ether  could  be  imagined  which  would  perform  these 
new  duties,  especially  as  it  was  already  staggering 
under  the  burdens  of  the  old  ones.  Faraday  proposed 
as  a  substitute,  that  we  should  no  longer  imagine  the 
medium  to  be  a  substance  having  material  or  mechani- 
cal properties,  but  one  responding  to  electrical  and 
magnetic  actions.  He  was  far  in  advance  of  his  time 
and  to  be  acceptable  the  hypothesis  needed  the  mathe- 
matical development  which  was  so  skillfully  accom- 
plished by  Maxwell.  Both  Faraday  and  Maxwell, 
while  really  destroying  the  material  nature  of  the  ether, 
strove  to  maintain  at  least  a  partial  connection  between 
electro-magnetic  and  mechanical  attributes.  For  this 
reason  they  supposed  that  electro-magnetic  stresses 
manifested  themselves  by  creating  mechanical  strains  in 
the  ether  and  in  matter  immersed  in  it.  Such  strains 
must  produce  actual  physical  deformations  of  size  and 
shape  in  all  electrified  bodies.  It  has  been  shown  ex- 
perimentally by  the  writer  that  such  deformations  are 
not  produced  in  electrified  matter  and  lately  Professor 
Lorentz  has  stated,  that  since  Helmholtz  proved  these 
stresses  would  cause  the  medium  to  move,  and  since  no 
experiment  has  ever  shown  us  a  trace  of  a  motion  in  the 
ether,  we  must  deny  the  real  existence  of  such  stresses. 
The  effect  of  such  a  denial  is  to  separate  all  attributes 
of  the  ether  from  concrete  realities  and  to  class  them 


162        THE  LIMITATIONS  OF  SCIENCE 

as  abstract  symbols.  Professor  Lorentz  is  quite  ex- 
plicit on  this  point,  as  he  holds  that,  "  while  thus  deny- 
ing the  real  existence  of  ether  stresses,  we  can  still 
avail  ourselves  of  all  the  mathematical  transformations 
by  which  the  application  of  the  formula  (for  these 
stresses)  may  be  made  easier:  .  .  .  and  for  conveni- 
ence's sake  we  may  continue  to  apply  to  the  quantities 
occurring  in  this  integral  the  name  of  stresses.  Only, 
we  must  be  aware  that  they  are  only  imaginary  ones, 
nothing  else  than  auxiliary  mathematical  quantities." 
This  dematerialization  of  the  ether,  when  it  was  once 
found  that  light  and  heat  still  managed  to  come  to  us 
from  the  sun  although  we  had  given  its  medium  of 
transmission  such  a  rude  shock,  has  progressed  rapidly 
until  to-day  many  accept  the  postulate  that  there  is  no 
difference  between  absolutely  vacuous  space  and  the 
ether,  except  that  the  latter  is  the  temporary  seat  of 
radiant  energy  and  possesses  a  light  vector.  If  this 
definition  of  space  means  anything,  it  implies  that  light 
has  the  power  of  changing  a  vacuum  into  a  substance. 
When  we  stop  to  think  that  a  vacuum  means  absolute 
negation  of  everything,  we  realize  what  an  extraordi- 
nary thing  light  is  in  modern  physics.  Just  consider 
this  statement  of  Professor  Einstein,  which  is  con- 
sidered almost  authoritative,  "  the  places  in  space 
where  these  electro-magnetic  actions  (i.e.,  light)  occur 
are  here  considered  not  as  states  of  a  sort  of  matter, 
but  as  self-existing  things  which  are  similar  to  ponder- 


CLASSICAL  AND  NEW  MECHANICS      163 

able  matter  and  in  common  with  it  have  the  character- 
istic of  inertia."  One  has  merely  to  ask,  what  becomes 
of  these  self-existing  things  when  light  ceases  to  go 
through  a  certain  space  and  it  slips  back  into  its  state 
of  vacuity? 

Without  going  into  details,  we  find  a  like  trend  in 
the  hypothesis  of  the  nature  of  matter.  It  began  with 
the  atom  as  a  minute  simulacrum  of  ponderable  bodies, 
and  then  we  proceeded  to  strip  away  one  concrete  at- 
tribute after  another  until  for  a  brief  interval  matter 
was  a  manifestation  of  an  entity,  electricity.  But 
even  this  idea  was  too  concrete,  too  material,  to  serve 
and  now  the  objective  universe  is  the  symbol,  energy. 

If  we  finally  subscribe  to  these  ideas,  are  we  not 
really  acknowledging  that  hypothetical  science  has 
failed  as  the  interpreter  of  an  objective  world?  It 
seems  to  me  the  guides  to  knowledge  are  now  to  be 
found  in  those  subjective  impressions  which  must 
depend  on  the  individual  and  vary  with  him.  Scientific 
laws  are  thus  not  facts  to  be  discovered  but  the  tempo- 
rary consensus  of  opinion  of  a  number  of  individuals 
who,  for  the  time  being,  find  themselves  in  agreement. 
The  classical  natural  philosophy  of  Newton  and  Gali- 
leo has  drifted  into  that  transcendental  symbolism 
which  is  apt  to  take  place  when  German  thinkers  be- 
come the  leaders  in  philosophy. 

Evidently  an  almost  chaotic  condition  had  de- 
veloped in  our  ideas  of  space,  matter,  and  electricity. 


164        THE  LIMITATIONS  OF  SCIENCE 

Each  theorist  advanced  an  hypothesis  of  the  most 
tentative  character  which  all  felt  to  be  inadequate. 
Yet,  in  spite  of  the  confusion,  three  points  of  agree- 
ment may  be  noted.  In  the  first  place,  the  ether  as  a 
material  substance  is  impossible  and  even  useless;  the 
name,  it  is  true,  is  left  but  it  expresses  now  but  the 
shadow  of  a  reality.  When  the  ether  is  called  an 
electro-magnetic  something,  or  a  space  differentiated 
only  by  the  transient  presence  of  energy,  the  name  may 
signify  something  but  it  is  hardly  intelligible  except  as 
a  mathematical  symbol.  Secondly,  these  theories 
agree  in  assuming  electricity  to  be  an  entity;  that  is, 
we  are  to  suppose  that  it  is  not  due  to  a  state  of  mat- 
ter, manifested  by  a  special  mechanical  force,  but  a 
substance  like  matter,  divisible  into  atomic  elements 
and  having  inertia.  Thirdly,  the  mass  inertia  of  mat- 
ter is  not  an  invariable  quantity  but  changes  with  the 
velocity  of  a  body;  thus  it  is  the  measure  of  matter 
only  while  there  is  no  motion. 

Such  was  the  state  of  physical  theory  when  Professor 
Einstein  announced,  in  an  article  published  in  the 
Annalen  der  Physik  for  the  year  1905,  a  new  scientific 
principle  which  he  believes  will  reconcile  the  contra- 
dictions of  our  new  hypotheses;  satisfy  the  three  con- 
ceptions mentioned;  and  correct  and  amplify  the  New- 
tonian mechanics  so  that  it  will  again  harmonize  with 
modern  science.  Whether  this  Principle  of  Relativity 
will  accomplish  all  that  its  discoverer  hopes  can  be 


CLASSICAL  AND  NEW  MECHANICS      165 

decided  only  after  an  exhaustive  trial.  But  there  is  no 
doubt  as  to  the  startling  effect  it  has  produced  on  scien- 
tific theory  nor  of  the  far-reaching  importance  of  its 
conclusions.  For  example,  Professor  Planck  of  Berlin 
is  said  to  have  declared  that  this  new  idea  of  time  and 
space  surpasses  in  boldness  anything  that  has  appeared 
up  to  the  present  time  in  speculative  science. 

The  name,  Principle  of  Relativity,  is  derived  from 
Professor  Einstein's  first  postulate,  which  is  as  fol- 
lows: the  idea  of  absolute  rest  or  absolute  motion  is 
an  impossibility  to  the  human  mind,  and  not  only  in 
mechanics,  but  also  in  electro-dynamics  corresponds 
to  no  properties  of  phenomena. 

In  addition  he  announced  as  a  second  postulate  that 
the  velocity  of  light,  V,  in  empty  space  is  an  absolute 
constant  of  nature.  Hence  this  velocity,  contrary  to 
all  others,  is  independent  of  the  motion  of  the  body 
emitting  and  of  the  one  receiving  the  light.  The 
startling  nature  of  this  postulate  is  readily  under- 
stood when  we  remember  that  the  closest  analogue  to 
light  is  sound,  the  velocity  of  which  is  known  by  ex- 
perience to  be  dependent  on  these  quantities. 

He  has  recorded  for  us,  that  he  became  convinced  of 
the  necessity  for  these  postulates,  because  the  theory 
of  electro-dynamics  developed  by  Maxwell  leads  to 
an  asymmetry,  when  applied  to  moving  bodies,  which 
is  not  true  experimentally.  For  instance,  when  a  mag- 
net and  an  electric  conductor  are  moved  with  respect 


166        THE  LIMITATIONS  OF  SCIENCE 

to  each  other,  the  phenomena  of  the  forces  developed 
are  observed  to  depend  only  on  the  relative  motion  of 
the  magnet  and  the  conductor,  but  Maxwell's  theory 
requires  a  different  explanation,  according  to  which  is 
moved  and  which  remains  at  rest.  Besides  this  dis- 
crepancy between  observation  and  theory,  experiments, 
devised  with  sufficient  accuracy,  fail  to  show  any  effect 
of  the  earth's  motion  through  space  on  the  phenomena 
of  light. 

It  will  be  convenient  to  grant  these  postulates  and 
follow  Professor  Einstein's  deductions  before  attempt- 
ing any  criticism.  In  the  first  place,  their  adoption 
does  away  with  the  possibility  of  an  ether  and  revives 
the  postulate  of  space  as  a  vacuum.  Both  theory  and 
experiment  show  that  an  ether,  if  there  be  one,  must 
be  in  absolute  rest  with  respect  to  the  motion  of  the 
earth,  and  the  first  postulate  denies  the  possibility  of 
absolute  rest  and  motion.  Again,  the  failure  of  New- 
tonian mechanics  lies  in  the  assumption,  which  is 
always  tacitly  made,  that  moving  bodies  are  subject 
to  the  same  mechanical  laws  as  those  at  rest.  As  I 
have  already  pointed  out,  the  modification  to  be  made 
in  the  laws  for  ordinary  bodies  is  very  minute  and 
would  probably  never  have  become  of  importance  if 
modern  theory  had  not  been  interested  in  the  properties 
of  bodies  moving  with  velocities  approximating  that  of 
light. 

vThe  root  of  the  error  in  the  mechanics  of  moving 


CLASSICAL  AND  NEW  MECHANICS      167 

bodies,  Professor  Einstein  believes,  lies  in  our  deter- 
mination of  time,  and  clear  thinking  in  regard  to  time 
is  nearly  all  that  is  necessary  to  clear  up  the  trouble. 
Suppose  a  body  or  a  material  point  to  be  at  rest  rela- 
tively to  a  coordinate  system  of  three  rectangular  lines, 
then  its  position  can  easily  be  determined  by  the  ordi- 
nary geometrical  method  of  measuring  its  distance 
from  each  of  the  lines  by  rigid  measuring-rods.  But 
if  the  point  is  in  motion  with  respect  to  the  reference- 
system,  its  position  depends  on  time  and  cannot  be 
determined  by  the  geometrical  method.  Our  idea  of 
time  is  usually  defined  by  what  we  call  isochron- 
ism;  we  say  an  event  occurs  at  seven  o'clock, 
when  the  occurrence  of  the  event  and  the  position  of 
the  hour-hand  of  a  clock  at  seven  are  simultaneous. 
But  suppose  the  clock  were  at  some  distance  from  us, 
then  we  could  observe  the  hand  to  be  at  seven  only 
after  it  had  passed  beyond  that  figure,  since  it  would 
take  some  time  by  any  method  of  transmission  for  the 
intelligence  to  reach  us.  As  the  velocity  of  light  is  the 
greatest  of  all  known  motions,  the  least  discrepancy 
would  be  caused  by  using  light  signals  as  the  mode 
of  transmitting  such  intelligence.  Also,  if  we  accept 
the  second  postulate,  our  intelligence  will  be  still  more 
accurate  because  the  velocity  of  light  is  unaffected  by 
other  motions  and  we  thus  avoid  the  difficulty  caused 
by  the  question  whether  any  relative  motion  between 
us  and  the  clock  is  an  approach  or  a  separation.  To 


168         THE  LIMITATIONS  OF  SCIENCE 

illustrate  further  our  confusion  as  regards  the  measure- 
ment of  time,  suppose  two  persons  wish  to  record  two 
events,  which  we  shall  grant  to  be  simultaneous, 
but  which  occur  at  different  places,  A  and  B.  An 
observer  at  A  records  the  event,  when  it  occurs  at  A, 
as  being  at  TA  time  by  his  clock,  and  instantly  signals 
the  fact  to  an  observer  at  B.  Whatever  the  means  of 
signaling,  a  certain  time  will  elapse  before  the  ob- 
server at  B  is  cognizant  of  it.  For  the  reasons  given, 
we  shall  adopt  light  signals  as  the  best  method.  B 
observes  the  signal  as  TB  time  by  a  clock  placed  at 
B  and  immediately  reflects  it  back  to  A,  who  receives 
it  at  T'A  time  by  his  clock.  Although  we  have  granted 
that  both  events  were  simultaneous,  it  is  evident  they 
will  not  be  so  recorded  by  the  two  observers.  B  will 
record  the  event  at  A  as  being  later  than  the  one  at  B. 
But  if  the  velocity  of  light  be  absolutely  independent 
of  all  conditions,  then  we  should  find  that  the  differ- 
ences of  time  going  and  returning  are  the  same,  or 
TB  — TA  =  T'A  —  TB .  This  relation  is  satisfied  by  any 
two  events  occurring  at  a  distance  from  each  other, 
is  Professor  Einstein's  definition  of  simultaneous 
events  or  isochronism.  The  definition  may  be  put  in 
this  form:  two  events  are  simultaneous,  if  the  differ- 
ence of  time  to  flash  a  signal  there  and  back  is  equal 
to  twice  the  distance  between  the  two  positions  divided 
by  the  velocity  of  light,  V. 

Not  only  does  this  limitation  in  our  ability  to  meas- 


CLASSICAL  AND  NEW  MECHANICS      169 

ure  time  affect  our  ideas  of  time,  but  it  also  has  an 
important  and  unsuspected  influence  on  our  ideas  of 
the  size  and  shape  of  a  body.  This  may  be  shown  by 
an  example.  Suppose  we  wish  to  measure  a  rigid  rod 
of  length,  /,  moving  in  the  direction  of  its  axis  with 
a  velocity,  v,  then  there  are  two  methods  of  measuring 
this  length  and  they  do  not  give  concordant  results. 

First  an  observer  may  move  with  the  rod  and  meas- 
ure its  length  by  applying  directly  to  it  a  measuring- 
rod.  He  will  evidently  obtain  the  same  result  as  if  both 
he  and  the  rod  were  at  rest. 

A  second  method  is  possible  and  is  frequently  em- 
ployed. An  observer  remains  at  rest  and  notes  the 
positions  of  the  two  ends  of  the  rod,  at  a  certain  time, 
t,  which  he  determines  by  means  of  clocks,  also  at  rest 
and  tested  for  synchronism.  These  two  points  are 
dependent  on  our  ability  to  record  simultaneous  events ; 
if  the  rod  were  at  rest  the  problem  would  be  the  one 
already  discussed,  but  in  this  case  the  rod  has  a  velocity, 
v,  and  consequently  the  time  used  in  signaling  in  one 
direction  involves,  V  —  v,  and  in  the  other,  V  +  v. 
So  when  he  measures  the  distance  between  the  two 
points,  which  may  also  be  called  the  length  of  the 
rod,  he  will  find  it  not  equal  to  /  as  determined  by  the 
first  method,  if  he  still  regards  his  clocks  as  isochro- 
nous; or  if  he  determined  two  positions  whose 
measured  distance  is  /  then  his  clocks  will  no  longer  be 
isochronous. 


170        THE  LIMITATIONS  OF  SCIENCE 

Now  our  measurements  of  length  are  usually  made 
under  the  condition  that  we,  clocks,  and  rods  are  all 
moving  with  the  earth  and  so  relatively  at  rest.  Our 
measurements  of  length  of  bodies  on  the  earth  are 
thus  different  from  those  which  would  be  made  on  the 
same  bodies  by  an  observer  if  he  could  be  stationed 
with  his  clocks  in  the  moon.  Also  if  an  object  on  the 
earth  is  measured  while  it  is  moving  with  respect  to 
the  observer,  it  will  appear  to  have  a  different  length 
from  that  which  it  has  when  relatively  at  rest.  Thus 
the  dimensions  of  a  body  are  dependent  on  its  velocity, 
and  Newtonian  mechanics,  which  assumes  the  con- 
trary, must  be  modified  when  applied  to  bodies  in 
motion. 

Professor  Einstein  then  derives  a  set  of  equations 
which  will  express  the  dimensions  of  a  moving  body 
as  they  appear  to  a  stationary  observer.  These  show 
that  the  length  of  every  body  moving  with  a  velocity, 
v,  is  diminished  in  the  direction  of  its  motion  by  the 
fraction 


and  that  its  dimensions  at  right  angles  to  its  mo- 
tion remain  unchanged.  Thus  a  sphere  in  motion 
becomes  an  ellipsoid  flattened  in  the  direction  of 
its  motion  by  an  amount  equal  to  the  above  frac- 
tion. It  is  proper  to  say,  that  this  effect  is  quite 
inappreciable  at  ordinary  velocities.  This  is  true  even 


CLASSICAL  AND  NEW  MECHANICS      171 

of  so  great  a  velocity  as  that  of  the  earth  around  the 
sun.  This  velocity  is  about  thirty  kilometers  per  sec- 
ond while  V  is  300,000  kilometers  per  second.  One 
diameter  of  the  earth  would  thus,  to  an  observer  in 
the  sun,  appear  shortened  about  7.5  centimeters,  or 
three  inches.  But  this  effect  becomes  quite  important 
for  velocities  approaching  one-tenth  of  V.  And  a 
velocity  equal  to  that  of  light  is  absolutely  unattain- 
able because  the  length  of  the  moving  body  would 
then  be  reduced  to  zero.  So  we  have  the  curious 
anomaly  of  a  finite  velocity  producing  an  infinite 
effect. 

The  same  equations  also  show  that  if  one  of  two 
clocks,  which  are  synchronous  when  at  rest,  be  moved 
with  a  velocity,  v,  the  stationary  clock  will  run  faster 
each  second  than  the  moving  one.  The  maximum 
value  of  the  difference  is  when  one  clock  runs  infinitely 
faster  than  the  other. 

We  must  not  lose  sight  of  the  fact  that  this  discus- 
sion, so  far  as  mechanical  bodies  and  motions  are  con- 
cerned, is  purely  academic,  because  for  them  the  ratio 
v/V  is  too  small  in  any  known  case  to  have  an  appre- 
ciable effect.  The  Principle  of  Relativity  has  its  great- 
est significance  when  applied  to  problems  in  electricity, 
provided  we  accept  the  theory  of  electrons.  //  the 
atom  of  matter  be  composed  of  particles  of  electricity, 
if  the  inertia  of  matter  be  variable  and  due  to  elec- 
trical reactions,  and  if  the  velocity  of  the  electron 


i;2        THE  LIMITATIONS  OF  SCIENCE 

approaches  that  of  light,  then  the  effect  of  its  velocity 
on  its  shape,  size,  and  mass  is  an  important  matter, 
For,  let  m  be  the  mass  of  an  electron  at  rest,  from 
Professor  Einstein's  formulae,  its  apparent  mass  in  the 
direction  of  motion  is 


m 


and  its  mass  at  right  angles  to  the  motion  which  would 
make  it  resist  change  of  direction  is 


m 


Thus  we  have  the  unusual  result  of  not  only  a  variable 
mass,  but  also  a  difference  in  mass  according  to  the 
direction  considered. 

Another  consequence  of  the  hypothesis  is,  that  mass 
also  depends  on  energy.  This  result  is  of  extraordi- 
nary importance,  for  it  means  we  have  no  ability  to 
distinguish  between  the  inertia  of  a  physical  system 
of  bodies  and  its  energy;  in  other  words,  between  the 
inertia  of  a  body  and  the  energy  content  of  the  space 
surrounding  it.  When  we  recall  Professor  Einstein's 
conception  of  space  and  energy,  which  I  have  quoted, 
most  persons  will  become  convinced  that  no  idea  of 
the  nature  of  matter  could  be  more  abstract.  The 
mass  of  a  single  body  thus  remains  constant  only  when 


CLASSICAL  AND  NEW  MECHANICS      173 

its  energy  remains  constant.  If  it  gives  out  heat, 
light,  or  electro-magnetic  energy,  or  if  it  even  moves, 
its  mass  continually  decreases,  until,  theoretically  at 
least,  it  would  melt  away  into  a  complex  of  energy :  I 
know  of  no  name  to  designate  so  immaterial  a  thing 
as  this  complex  of  energy  located  somewhere  in  vacu- 
ous space.  To  be  sure,  this  interchange  between  mass 
and  energy  is  very  slow,  so  slow  that  ordinary  minds 
grow  skeptical  of  its  existence.  Thus  a  body  radiat- 
ing enough  heat  to  warm  a  kilogram  of  water,  one 
degree  Centigrade,  would  decrease  in  mass  only  about 
4.6  X  io~n  grammes.  It  is  fortunate  that  mass  dis- 
sipates so  slowly  or  we  should  indeed  be  things  dreams 
are  made  of. 

The  last  deduction  I  shall  note  is  that  the  tem- 
perature of  a  moving  body  is  less  when  measured  by 
a  moving  observer  than  by  one  who  is  stationary. 

Such  are  some  of  the  more  startling  conclusions 
which  have  been  derived  from  the  Principle  of  Rela- 
tivity. If  they  can  be  established,  and  men  be  per- 
suaded that  the  universe  is,  or  even  may  be,  as  they 
indicate,  a  revolution  has  been  accomplished  in  scien- 
tific thought.  If  we  are  to  criticise  the  conclusions  of 
this  hypothesis,  and  they  are  opposed  to  what  seems 
reasonable,  it  must  be  done  by  examining  the  postu- 
lates; in  them,  as  in  all  hypotheses,  lies  the  real 
strength  or  weakness  of  the  system. 

Professor  Einstein  asks  us  to  accept  two  postulates. 


174        THE  LIMITATIONS  OF  SCIENCE 

The  first  is;  we  have  no  ability  in  us  to  determine 
absolute  rest  or  motion.  We  can  say  only  that  one 
body  is  at  rest  or  changes  position  with  respect  to 
others.  Phenomena  are  conditioned  entirely  by  the 
relative  positions  of  bodies  and  we  can  gain  nothing 
toward  an  explanation  by  introducing  the  idea  of  abso- 
lute position.  The  second  postulate  is;  the  velocity 
of  light,  V,  is  a  universal  and  absolute  constant. 

Apparently  no  objection  has  been  made  to  his  state- 
ment that  these  two  postulates  are  sufficient  from 
which  to  derive  all  the  conclusions  mentioned.  But  it 
seems  to  me,  at  least  two  more  independent  postulates 
are  advanced  in  the  memoir  on  relativity,  which  must 
also  be  granted.  I  shall  propose  as  a  third,  Professor 
Einstein's  definition  of  time,  and  as  a  fourth,  the  as- 
sumption of  the  atomic  nature  of  electricity.  The 
fourth  postulate  carries  with  it  as  corollaries,  that  the 
amount  of  electricity  per  atom,  or  the  electron  as  it  is 
called,  is  a  universal  constant,  and  that  the  mass  of  the 
electron  is  variable.  My  excuse  for  offering  them  is, 
they  cannot  be  derived  from  his  postulates,  and  his  con- 
clusions require  them. 

The  first  postulate  can  be  granted  at  once  and  unre- 
servedly for  all  purely  mechanical  motions  of  bodies. 
These  involve  merely  changes  of  position  and  do  not 
affect  the  nature  of  bodies  nor  their  phenomena.  But 
it  must  be  accepted  with  limitations  when  in  addition 
to  mechanical  motion,  and  by  mechanical  motion  I 


CLASSICAL  AND  NEW  MECHANICS      175 

mean  a  mere  change  of  position,  one  body  is  emitting 
energy  in  the  form  of  heat,  light,  or  electricity,  and  the 
other  receiving  it.  True  relativity  requires  a  strictly 
symmetrical  arrangement.  Now  the  mechanical  mo- 
tions of  two  bodies  with  respect  to  one  another  are 
symmetrical.  If  a  body  has  a  velocity,  Vi,  to  the  right 
and  another  a  velocity,  v2,  to  the  left,  they  approach 
each  other  with  a  velocity,  Vi  +  v2.  The  same  result  is 
obtained  if  the  velocities  of  the  bodies  are  interchanged. 
This  symmetry  is  not  true  if  the  first  body  is  emitting 
energy  and  the  second  receiving  it.  The  behavior  of 
each  is  then  conditioned  by  the  behavior  of  the  other 
and  in  an  asymmetrical  manner.  As  an  illustration: 
let  a  body  by  a  periodic  disturbance  of  its  parts  send 
out  a  wave  of  heat;  this  proceeds,  according  to  theory, 
through  space  in  all  directions  and  on  encountering  a 
second  body  produces  a  periodic  disturbance  in  it.  The 
effect  of  this  energy  is  twofold;  the  motions  of  the 
parts  of  the  two  bodies  are  symmetrical  but  the  wave 
itself  does  not  proceed  from  the  second  body  in  all 
directions  but  only  in  the  one  already  impressed  upon 
it  by  the  first  body.  To  make  this  clearer,  we  may  start 
a  wave  along  a  stretch  of  string  by  plucking  aside  one 
part  of  it;  the  wave  will  travel  from  the  initial  point 
along  the  string  in  two  directions,  causing  successive 
parts  to  vibrate  symmetrically,  but  these  parts  will 
send*  the  wave  in  one  direction  only.  So  we  may  say 
the  velocities  of  two  bodies  are  relative  because  the 


i;6        THE  LIMITATIONS  OF  SCIENCE 

quantities  appear  in  the  mathematical  expression  in  a 
symmetrical  manner ;  so  also  are  their  momenta  or  their 
masses  multiplied  by  their  velocities.  But  this  is  not 
the  case  for  energy  since  it  involves  the  square  of  the 
velocity.  The  squared  velocity  remains  positive  al- 
though we  change  direction  and  the  composition  of  two 
energies  is  always  an  addition.  For  true  relativity,  a 
change  in  direction  must  be  accompanied  by  a  change 
in  sign.  The  extension  of  the  idea  of  relativity  to  in- 
volve cases  of  radiant  energy  is  partly  responsible 
for  the  conclusion  that  mass  is  a  function  of  energy. 

Professor  Einstein's  second  postulate  has  been 
widely  discussed  and  many  attempts  have  been  made  to 
interpret  it.  At  first  sight  it  seems  absurd  to  say  that 
the  mechanical  motion  of  a  body  emitting  light 
does  not  affect  the  velocity  of  the  light  emitted.  But 
the  fact  remains  that  all  our  experiments,  and  they 
have  been  most  accurate  and  searching,  fail  to  find 
any  difference  in  the  velocity  of  light  whether  the 
sources  and  the  recipient  are  at  rest  or  in  motion.  As 
we  have  seen,  Professor  Einstein,  with  admirable 
directness,  goes  straight  to  the  point:  he  accepts  the 
reliability  of  these  experiments;  assumes  the  constancy 
of  V  as  a  postulate,  determines  its  effect  on  the  space 
dimensions  of  bodies  and  on  time,  and  finds  that  we 
must  change  our  previous  ideas  of  these  radically.  Let 
us,  when  discussing  V,  consider  it  under  two  heads: 
first,  when  light  passes  through  transparent  material 


CLASSICAL  AND  NEW  MECHANICS      177 

bodies  and  is  subject  to  experimental  verification;  sec- 
ondly, when  it  passes  through  space  absolutely  de- 
prived of  material  bodies  and  so  is  not  subject  to 
experimental  evidence. 

In  the  first  case,  we  know  that  there  is  a  true  path 
and  that  light  moves  very  approximately  in  straight 
lines,  and  we  have  quite  accurately  measured  the  time 
light  requires  to  move  from  one  place  to  another 
through  various  substances.  V  is  here  the  length  of 
path  divided  by  the  time, — a  true  velocity.  We  know 
that  this  V  is  a  variable ;  it  is  less  in  water  than  it  is  in 
air,  and  still  less  in  glass.  It  is  also  less  in  dense  air 
than  in  rarefied  air.  Not  only  does  V  vary  with  the 
kind  of  matter  through  which  light  passes,  but  it  also 
depends  on  the  motion  of  the  medium  as  shown  in  the 
experiments  on  the  velocity  of  light  passing  through 
columns  of  moving  water  made  by  Fizeau  and  repeated 
by  Professor  Michelson.  The  velocity  of  light  in 
material  media  is  therefore  subject  to  all  the  variations 
which  influence  the  velocity  of  sound  and  other  types 
of  motion  and  evidently  cannot  be  the  V  assumed  by 
Professor  Einstein  to  be  an  absolute  constant. 

He  must  then  limit  his  postulate  strictly  to  what  is 
called  the  velocity  of  light  in  absolutely  immaterial 
space.  There  are  two  methods  of  obtaining  this  value. 
We  observe  the  difference  in  time  between  the  cal- 
culated eclipse  of  some  satellite  and  the  recorded  ob- 
servation of  the  event  or  we  use  other  stellar  phe- 


i;8        THE  LIMITATIONS  OF  SCIENCE 

nomena.  If  we  know  the  distance  and  the  time,  we 
say  the  velocity  of  light  in  empty  space  is  the  quotient 
of  the  two.  Such  observations  are  quite  inadequate 
to  settle  experimentally  the  question  of  the  constancy 
of  V.  Our  measurements  of  the  distances  are  crude 
for  such  a  purpose,  and  also  the  light  must  travel  part 
of  the  way  through  a  material  medium  such  as  the  air. 
Neglecting  such  astronomical  methods,  we  have  left 
only  determinations  of  V  made  on  the  earth  where 
the  path  is  necessarily  through  matter.  Here,  what  we 
are  to  call  the  constant  V  can  be  found  only  by  extra- 
polation. For  example,  we  find  that  the  ratio  of  the 
velocity  in  air  and  in  water  is  about  four  to  three  and 
agrees  with  their  refractive  indices.  We  find  also  that 
the  velocity  in  different  gases  as  they  are  reduced  in 
density  tends  to  a  common  value,  which  is  independent 
of  the  kind  of  gas  and  approaches  the  value  3  x  io10 
centimeters.  If  we  take  this  extrapolated  value  of 
3  x  io10  centimeters  for  the  velocity  of  light  in  empty 
space  and  assume  the  refractive  index  of  space  to  be 
one,  then  we  may  calculate  back  and  by  this  method  we 
find  the  absolute  refractive  index  of  air  at  ordinary 
pressure  to  be  1.0002.  Such  an  experimental  method 
and  such  reasoning  are  highly  unsatisfactory.  In  the 
first  place,  we  start  with  measurements  of  lengths  and 
time  which  are  subject  to  experimental  verification  and 
calculate  V,  from  these  we  pass  to  a  supposititious  V 
where  only  one  factor,  the  time,  is  subject  to  experi- 


CLASSICAL  AND  NEW  MECHANICS      179 

mental  proof  and  the  other  factor,  the  length,  is  not,  as 
we  cannot  experiment  on  the  path  of  light  in  free  space. 
But  passing  this  objection,  we  have  calculated  from 
length  and  time  determinations  a  value  for  V  and  Pro- 
fessor Einstein  declares  it  to  be  an  absolute  constant. 
He  then  reasons  backward  that  the  length  of  a  body 
and  time  determinations  must  be  variables  with  motion, 
in  order  to  keep  V  constant.  Of  course,  if  Professor 
Einstein  wishes  to  look  on  the  universe  as  a  purely  ab- 
stract conception;  and  if  he  wishes  to  make  what  we 
sometimes  call  concrete  or  objective  phenomena  cor- 
respond to  his  preconceived  idea  of  the  universe,  he 
can  assume  V  in  a  vacuum  to  be  a  universal  and  ab- 
solute constant  and  no  one  can  disprove  it  sci- 
entifically. But  there  are  some  who  still  cling  to 
the  idea  that  dimensions  of  bodies  and  time  are 
not  subject  to  our  fancy,  and  who  believe  that 
if  any  quantities  must  vary,  it  should  be  those 
which  we  have  no  means  of  determining  directly. 
And  after  all  it  is  asking  a  great  deal  of  us,  to 
upset  our  ideas  in  order  to  explain  at  bottom  a 
single  experiment,  that  of  Michelson  and  Morley,  how- 
ever accurately  it  has  been  performed  and  however 
puzzling  its  results  may  be.  He  has  not  even  the 
justification  his  predecessors  would  have  had.  When 
the  ether  was  believed  to  be  a  crystalline  solid  which 
vibrated  with  the  passage  of  light  rays,  V  had  a  real 
meaning  although  we  could  not  determine  it  directly. 


i8o        THE  LIMITATIONS  OF  SCIENCE 

When  the  ether  was  a  substance  which  periodically 
varied  electromagnetically,  we  could  still  say  that  V 
had  a  possible  meaning.  But  the  latest  definition,  that 
the  ether  is  absolutely  quiescent  space  to  be  distin- 
guished from  vacuous  space  only  by  the  fact  that  it  is 
the  seat  of  an  entity,  called  electro-magnetic  energy, 
and  contains  a  light  vector,  makes  the  word  velocity 
when  applied  to  V  absolutely  without  meaning  in  any 
ordinary  sense  of  the  term.  To  speak  of  a  motion  in 
an  absolutely  quiescent  space  is  a  rather  startling  state- 
ment. The  ether  also  becomes  a  local  affair,  shifting 
back  and  forth  in  vacuous  space  according  as  light  is 
present  or  not.  The  feeble  light  of  a  candle,  appa- 
rently, changes  nothing  into  something. 

But  aside  from  these  considerations,  which  lie  in  the 
debatable  land  and  which  will  be  decided  largely  by  the 
temperament  of  the  individual,  there  seems  to  be  an 
absolute  contradiction  between  the  first  two  postulates 
as  I  understand  them.  If  V  be  the  value  of  the  velocity 
of  light  in  an  absolutely  quiescent  ether  and  itself  a 
constant,  then  the  velocity  of  light  in  a  material  me- 
dium, such  as  air,  is  an  absolute  velocity  or  motion 
when  referred  to  V.  Now  the  first  postulate  declares 
that  we  can  have  no  knowledge  of  absolute  motion 
and,  in  addition,  that  the  explanation  of  phenomena  is 
not  conditioned  by  absolute  motion. 

The  third  postulate,  which  I  have  proposed  as  neces- 
sary for  the  system  proposed  by  Professor  Einstein, 


CLASSICAL  AND  NEW  MECHANICS      181 

is  his  definition  of  time.  He  says, — our  idea  of  time 
is  defined  by  synchronism  or  the  simultaneous  occur- 
rence of  an  event  and  the  position  of  the  hour-hand 
of  a  clock  at  a  certain  position,  the  number  seven  for 
example.  This  is  certainly  not  our  idea  of  time  but 
merely  our  method  of  measuring  it  quantitatively.  If 
we  did  not  have  an  adequate  idea  of  time  as  the  mere 
succession  of  events,  we  should  have  no  conception  of 
what  simultaneous  occurrences  are  nor  of  how  to 
measure  time.  His  definition  gives  me  the  feeling 
that  if  I  could  make  clocks  go 'slower  my  life  would 
become  longer.  In  the  review  of  his  memoir,  it  was 
pointed  out  that  his  definition  of  simultaneity  or  isoch- 
ronism,  when  combined  with  the  constancy  of  V,  led 
to  the  conclusion  that  two  clocks  which  were  syn- 
chronous, when  relatively  at  rest,  would  not  remain  so, 
if  one  of  them  were  given  a  velocity.  Moreover  the 
length  of  a  body  in  motion  decreases  with  respect  to 
its  length  when  at  rest.  It  is  certain  that  these  re- 
sults depend  on  the  constancy  of  V.  If  we  are  willing 
to  rest  our  knowledge  of  time  and  space  on  a  value 
which  by  the  nature  of  things  can  never  be  put  to  a 
direct  test,  I  am  convinced  of  the  theoretical  correct- 
ness of  these  results.  But  I  am  not  willing  to  do  this. 
I  prefer  to  trust  to  the  invariability  of  time  and  space 
phenomena,  even  if  it  requires  V  to  be  a  variable  and 
time  measurements  to  contain  an  unavoidable  dis- 
crepancy. By  so  doing,  I  am  aware  that  I  forfeit  an 


182        THE  LIMITATIONS  OF  SCIENCE 

explanation  of  the  Michelson-Morley  effect  and  of 
some  others,  but  this  loss  is  not  overwhelming  and  we 
can  afford  to  wait  for  an  explanation  until  a  future 
time. 

I  am  the  more  willing  to  take  this  attitude,  because 
I  can  see  no  means  of  applying  the  Principle  of  Rela- 
tivity to  the  test  of  experience.  As  we  have  seen,  the 
velocity  of  light  in  any  material  medium  is  a  variable 
and  can  be  no  more  trusted  than  the  velocity  of  sound. 

Perhaps  this  illustration  may  make  my  meaning 
clearer.  Suppose  a  race  of  men  to  exist  who  are  blind 
and  have  no  knowledge  of  electro-magnetic  radiation, 
but  who  wish  to  measure  the  lengths  of  moving  bodies. 
They  will  undoubtedly  be  compelled  to  get  this  in- 
formation and  that  of  the  synchronism  of  clocks  by 
sound  signals.  It  is  evident  that  observations  car- 
ried out  under  conditions  similar  to  those  imposed  by 
Professor  Einstein  would  indicate  that  the  length  of 
a  moving  body  underwent  changes.  And  while  they 
could  make  corrections  for  some  of  the  effects,  because 
sound  waves  are  largely  affected  by  the  motion  of 
media  and  of  sonorous  bodies,  yet  they  would  undoubt- 
edly come  to  the  conclusion  that  the  dimensions  of  a 
moving  body  depended  to  some  extent  on  its  motion. 
Now,  if  we  should  bestow  sight  on  one  of  these  men,  he 
would  be  able  to  correct  their  measurements;  as  he 
could  by  his  immensely  more  rapid  light  signals  gain  a 
much  more  nearly  instantaneous  value  for  synchronism. 


CLASSICAL  AND  NEW  MECHANICS      183 

We  are,  at  present,  in  the  condition  of  this  man.  As  we 
improve  in  our  ability  to  measure  the  velocity  of  light 
under  different  conditions  we  shall,  Professor  Ein- 
stein thinks,  get  closer  to  the  knowledge  of  the  abso- 
lute V  and  to  the  relations  for  space  and  time  which 
he  has  derived.  But  we  may  suppose  men  will  some 
day  find  a  kind  of  radiation  which  has  a  velocity 
greater  than  V  (for  example,  the  transmission  of 
gravitation),  and  by  its  aid  remove  the  conviction  re- 
maining in  our  minds  that  motion  affects  length  and 
time.  Calculation  may  show  that  material  bodies  can- 
not attain  this  velocity,  but  we  are  speaking  of  an 
immaterial  radiation.  To  say  that  such  a  radiation  is 
impossible  is  as  futile,  at  least  as  unscientific,  as  for  a 
race  of  the  blind  to  say  that  there  is  no  light. 

Since  the  motion  of  any  ponderable  body  is  too  slow 
to  make  the  ratio  Vv  an  appreciable  quantity,  the  only 
supposable  case,  where  this  ratio  can  enter  as  a  deter- 
mining factor,  is  in  problems  of  radio-activity  and  the 
discharge  of  electricity  through  gases.  In  these,  the 
particles  of  matter  are  supposed  to  be  so  small  and  to 
have  a  velocity  so  great  that  their  mass  and  size  are 
measurable  functions  of  their  velocity.  But  to  limit 
the  applicability  of  the  principle  of  relativity  to  such 
supposititious  bodies  as  electrons,  is  to  rob  it  of  its  im- 
portance, and  we  should  hardly  consider  it  one  of  the 
great  principles  of  nature. 

But  even  this  is  not  all:  if  we  wish  to  apply  the 


184         THE  LIMITATIONS  OF  SCIENCE 

principle  to  electrons,  we  shall  need  a  fourth  postulate. 
We  must  assume  that  a  quantity  of  electricity  is 
atomic  in  character;  either  the  charge  of  electricity 
associated  with  what  we  call  an  atom  of  matter  is  an 
invariable,  or,  as  it  is  now  usually  expressed,  elec- 
tricity is  an  entity  which  may  be  divided  into  invariable, 
equal,  and  indivisible  parts  called  electrons.  As  a 
corollary  to  this  postulate,  the  ponderable  mass  of  an 
atom  is  a  variable  depending  on  its  velocity.  It  has 
been  shown  that  the  constancy  of  electric  quantity  and 
the  variability  of  mass  is  not  a  necessary  assumption. 
All  experiments,  which  involve  both  these  quantities, 
include  them  in  the  form  of  a  simple  ratio,  e/m ;  where 
e  is  the  quantity  of  electricity  and  m  the  mass  of  the 
electron.  It  is  evident  that  any  value  may  be  given 
to  this  ratio  by  supposing  either  one  of  its  members 
to  remain  constant  and  the  other  to  vary,  or  by  sup- 
posing both  to  vary  in  opposite  fashions,  and  it  is  just 
as  reasonable  to  keep  m  constant  and  to  let  e  vary  with 
the  velocity,  as  to  make  the  contrary  assumption.  This 
is  certainly  possible  until  we  have  experimental  evi- 
dence which  will  determine  our  decision,  and  this  evi- 
dence is  not  likely  ever  to  be  at  our  disposal. 

If  we  attempt  to  estimate  the  results  which  follow 
from  the  postulates  of  relativity,  the  first  would  be  that 
Professor  Einstein  has  proved  that  we  cannot  theoret- 
ically measure  in  space  and  time  moving  bodies  exactly 
by  the  laws  which  apply  to  bodies  at  rest.  The  first 


CLASSICAL  AND  NEW  MECHANICS      185 

postulate  will  be  accepted  for  all  mechanical  motions 
and  no  further  attempts  should  be  made  to  find  experi- 
mentally an  absolute  motion.  But  the  second  postulate 
contradicts  the  principle  of  relativity,  if  by  V  we  mean 
the  absolute  motion  of  something, — matter,  energy, 
or  light  through  quiescent  space.  If,  on  the  other 
hand,  V  is  understood  to  be  the  velocity  of  light  in 
space  containing  matter,  then  it  cannot  be  taken  as 
a  universal  constant.  The  third  postulate  concerning 
time  should  not  cause  us  to  change  our  belief  that  the 
dimensions  of  a  body  and  the  unit  of  time  are  inde- 
pendent of  velocity,  but  it  should  show  us  how  to  cor- 
rect our  measurements  of  moving  bodies,  as  we  must 
correct  all  subjective  measurements  of  objective  phe- 
nomena. 

If  we  grant  the  assumptions  of  Professor  Einstein, 
the  theory  of  relativity  is  a  perfectly  logical  system  so 
long  as  we  apply  it  to  abstract  systems  moving  with  a 
constant  velocity  in  a  straight  line.  But  I  can  find  no 
evidence  that  the  postulates  agree  with  experimental 
facts  and  certainly,  to  the  present  time  at  least,  its 
conclusions  will  not  affect  experimentally  the  laws  of 
mechanics.  Also  its  theoretical  conclusions  are  limited, 
as  yet,  to  the  rare  cases  when  there  is  neither  any 
change  of  speed  nor  of  direction.  We  should  remem- 
ber before  we  abandon  or  modify  Newtonian  mechanics 
that  mathematicians  have  devised  numerous  systems 
which  point  to  different  mechanical  laws.  If  we  pos- 


186        THE  LIMITATIONS  OF  SCIENCE 

tulate  a  fourth  dimension  to  space  we  can  deduce  per- 
fectly logical  laws  for  a  mechanical  system  that  are 
quite  different  from  the  laws  of  ordinary  mechanics. 
And  the  universe,  constructed  on  this  principle,  is  a 
very  beautiful  and  interesting  one.  It  is  the  privilege 
of  mathematicians  to  deal  with  symbols;  the  physical 
universe  is  no  more  important  to  them  than  any  other 
universe  which  can  be  developed  symbolically.  The 
trouble  occurs  when  the  distinction  between  the  real  or 
physical  universe  and  symbolical  or  metaphysical  uni- 
verses is  obliterated  in  the  minds  of  men  of  science. 


CHAPTER  VI 
SKEPTICISM  AND  IDOLATRY  IN  SCIENCE 

E  egli  questo  un  far  loro  oracolo  una  statua  di  legno,  e  a 
quella  correr  per  i  responsi,  quella  temere,  quella  riverire,  quella 
adorare. — GALILEO. 

THE  intellectual  habits  of  men  have  a  very  decided 
effect  on  their  characters,  and  it  is  evident  that  Galileo 
had  met  with  contemporaries  who  carried  their  devo- 
tion to  the  hypothetical  and  dogmatic  scientific  method 
of  Aristotle  to  a  state  of  idolatry,  accepting  on  faith 
that  which  should  be  submitted  to  experience.  The 
quotation,  from  his  Dialogues  on  the  Two  Principal 
^Systems,  which  I  have  given  expresses  his  opposition  to 
such  idolatry  in  no  uncertain  language.  It  is  fortunate 
for  me  that  I  wrote  this  chapter  as  an  essay  with  the 
same  title  before  I  had  read  Galileo's  comment,  because 
the  quotation  is  so  ben  trovato  that  otherwise  I  should 
have  been  accused  of  fitting  an  argument  to  a  title. 

Men  of  science  have  two  principal  functions  to  per- 
form: first  to  observe  the  phenomena  of  the  world; 
and  when  certain  connections  and  differences  are 
found  in  these  phenomena,  to  classify  them  under  laws. 
The  conclusions,  thus  derived,  have  been  used  with 
great  success  to  enlarge  our  intellectual  life;  to  modify 

187 


i88         THE  LIMITATIONS  OF  SCIENCE 

our  environment;  and  to  promote  our  comfort  and 
power.  But,  allured  by  their  great  and  legitimate  suc- 
cess in  these  two  fields  of  activity,  they  have  also  tried 
to  discover  the  hidden  causes  of  phenomena,  with  the 
result  that  a  sort  of  fictitious  world  has  been  created 
by  them,  in  which  the  laws  of  objective,  or  physical, 
phenomena  are  inextricably  confounded  with  the  de- 
ductions of  subjective  psychology.  Science  is  made 
metaphysical,  and  at  the  same  time  pretends  to  sup- 
plant metaphysics. 

This  encroachment,  naturally,  has  not  been  accom- 
plished without  a  sharp  conflict,  and  the  history  of 
the  nineteenth  century  is  permeated  with  the  struggle 
of  science  against  religion  and  philosophy.  The  issue 
was  clearly  in  favor  of  science,  which  has  not  only 
gradually  become  a  dominating  influence  in  education 
and  in  thought,  but  has  also  changed  our  attitude  to- 
wards history,  politics,  and  social  life  to  such  an  extent 
that  these  subjects  are  now  classed  as  sciences.  Even 
philosophy  and  religion  were  unsettled  by  its  growing 
power;  instead  of  basing  character  on  attributes  pecu- 
liar to  man  and  designated  by  the  name  of  spiritual 
powers,  many  now  include  man  with  the  rest  of  organic 
life  as  subject  only  to  the  statistical  and  impersonal 
laws  of  heredity  and  environment :  metaphysics  tends 
towards  a  philosophy  of  science;  religion  to  eugenics. 

Both  the  conflict  and  the  victory  were  no  doubt  in- 
evitable. But  the  results  have  not  been  on  the  whole 


SKEPTICISM  AND  IDOLATRY  189 

beneficial  either  to  society  or  to  science.  It  would  be 
difficult  to  prove  that  the  acceptance  of  the  belief  that 
man  has  no  divinity,  in  at  least  the  sense  of  super- 
natural powers,  and  no  innate  standards  of  right  and 
wrong — in  other  words,  that  he  is  merely  the  most 
complex  machine  in  a  world  governed  exclusively  by 
physical  and  chemical  laws — that  such  a  belief  has  not 
sunk  him  to  a  lower  plane  of  morality  and  induced 
in  him  a  resigned  weariness  towards  such  a  fate. 
The  victory  has  not  only  reacted  on  science  in  such  a 
way  as  to  give  the  world  a  too  implicit  confidence  in 
its  hypotheses,  but  it  has  also  made  men  of  science 
dogmatic  and  rash  in  proposing  bold  and  unsupported 
speculations, — impatient  of  criticism  of  themselves  and 
hypercritical  towards  religion,  philosophy,  and  all 
other  methods  of  human  thought.  Thus  the  most 
urgent  need  is  a  severe  and  just  criticism,  not  of  our 
experimental  observations  or  of  our  logic,  but  of  our 
hypotheses.  One  of  the  greatest  difficulties  in  de- 
veloping such  a  criticism  lies  in  the  fact  that  so  few 
men  of  science  leave  any  record  of  their  intimate  and 
personal  convictions  as  to  the  limitations  and  the  pos- 
sibilities of  their  field  of  action.  They  content  them- 
selves, for  the  most  part,  with  a  mere  statement  of 
experimental  results,  or  they  develop  speculative 
theories  without  much  consideration  whether  they  are 
fanciful  or  whether  their  influence  will  be  good  or 
pernicious.  Such  criticism  as  there  may  be  is  directed 


190         THE  LIMITATIONS  OF  SCIENCE 

towards  checking  the  accuracy  of  observation  and  the 
logic  of  deduction.  As  for  hypothesis,  there  is  a  gen- 
erally accepted  and  naive  belief  that  any  such  endeavor 
is  beneficial. 

The  writings  of  men  of  genius  in  science  frequently 
exhibit  this  sort  of  naivete  in  method  of  thought.  And 
probably  a  too  critical  attitude  would  be  a  hindrance 
to  their  creative  powers  as  they  must  look  at  problems 
intensively,  and  exclude  the  many  complexities  and 
doubts  which  would  tend  to  embarrass  them  in  their 
special  work.  It  would  be  foolish  to  say  "  thus  and 
thus  only  shall  a  man  work  out  his  ideas."  We  have 
an  Ampere  who  develops  the  laws  of  electro-dynamics 
from  the  experimental  facts  of  electricity,  and  quite  in- 
dependently of  the  prevailing  hypothesis  of  the  nature 
of  electricity;  and,  on  the  other  hand,  a  Lord  Kelvin 
who  could  not  work  until  he  had  first  visualized  a 
problem,  and  usually  he  put  this  image  into  a  concrete 
form,  making  for  the  purpose  many  different  models 
of  atoms  out  of  sticks  and  strings,  to  illustrate  the 
properties  of  matter. 

But  science  has  other  functions  in  addition  to  the 
attack  and  solution  of  problems  by  the  creative  power 
of  the  individual :  phenomena  and  laws  must  be  taught 
in  detail  to  the  specialist;  general  conclusions  must  be 
given  to  the  world  in  order  that  they  may  become  a 
part  of  the  general  intellectual  life;  and  finally  dis- 
coveries are  to  be  applied  to  social  and  industrial  needs. 


SKEPTICISM  AND  IDOLATRY  191 

Thus,  not  only  the  results  obtained  by  creative  minds, 
but  also  the  methods  of  obtaining  them,  are  important, 
because  they  will  ultimately  be  interpreted  and  pro- 
mulgated to  others.  The  harm  done  by  a  vicious 
method  of  thought  may  outweigh  the  benefits  of  a 
useful  discovery  happened  upon  in  spite  of  them. 
There  is  always  this  danger  in  the  hypothetical  method; 
the  man  who  assists  his  intellectual  labors  by  the  help 
of  crude  mechanical  models  undoubtedly  tries  to  keep 
distinct  in  his  mind  the  real  actions  of  nature  from 
the  properties  of  his  model,  let  us  say  of  the  atom. 
But  in  imparting  his  results  to  others,  this  model  is 
made  to  assume  an  aspect  of  reality  in  the  written  word 
which  was  not  in  his  own  mind.  Baffled  by  the  diffi- 
culty of  expressing  complicated  ideas,  he  paints  his 
metaphorical  pictures  too  vividly.  The  process  grows 
more  pronounced  as  the  idea  passes  from  mind  to 
mind;  the  fictitious  model  grows  progressively  more 
and  more  concrete,  until  to  the  student  and  to  the  world, 
it  is  at  last  the  concrete  model  of  the  atom  that  be- 
comes the  reality,  while  real  matter  dissolves  into  an 
abstraction.  And  if  words  can  be  relied  on  to  express 
ideas,  the  creator  of  the  atom  himself  is  a  believer 
in  the  reality  of  that  creation  of  his  imagination,  the 
model. 

This  sort  of  speculation  is  probably  least  dangerous 
in  pure  mathematics.  The  mathematician  looks  upon 
the  world  symbolically.  He  studies  its  laws  from  pos- 


192        THE  LIMITATIONS  OF  SCIENCE 

tulates  which  are  given  to  him  by  others,  or  assumed 
by  himself.  Thus  he  may  derive  the  laws  of  mechanics 
from  a  postulate  that  bodies  have  three  spatial  dimen- 
sions, which  is  verified  by  observation;  but  he  is  also 
interested  in  the  mechanics  of  bodies  which  would 
prevail  if  there  were  four  dimensions  to  space,  a  pos- 
tulate not  verifiable.  He  develops  a  geometry  which 
requires  the  axiom  that  parallel  lines  do  not  inter- 
sect ;  and  at  the  same  time  he  studies  another  geometry 
based  on  the  axiom  that  parallel  lines  do  intersect.  He 
finds  it  no  more  important  as  an  exercise  in  analysis 
to  study  a  solar  system -which  is  subservient  to  forces 
of  attraction,  than  one  which  obeys  a  law  of  repulsion. 
That  is,  he  is  not  limited  at  all  to  what  we  call  the 
reality  of  an  objective  and  material  world,  and  mathe- 
matical deductions  regarding  an  imaginative  world  will 
have  very  little  influence  on  society.  So,  also,  the 
purely  hypothetical  parts  of  such  abstract  subjects  as 
physics,  chemistry,  and  astronomy  are  not  very  influ- 
ential in  a  direct  manner,  but  indirectly  they  have  had 
an  enormous  influence  since  they  have  been  taken 
as  an  example  for  the  development  of  biology  and  that 
class  of  sciences  known  as  political  and  social.  Specu- 
lations in  these  subjects  have  a  direct  and  intimate 
bearing  on  the  character  of  the  individual  and  on  so- 
ciety. Thus  a  ready  proneness  to  accept  hypothesis 
and  speculation  as  well  as  observation  has  resulted 
in  the  crude  laws  and  dogmas  of  eugenics,  and  has  put 


SKEPTICISM  AND  IDOLATRY  193 

government  under  the  necessity  of  hearkening  to  the 
dilettante  of  the  slums,  and  the  feminist;  all  of  whom 
are  preaching  the  scientific  basis  of  their  nostrums.  It 
is  not  then  a  matter  of  indifference  what  the  hypotheses 
of  even  the  abstract  sciences  may  be,  or  how  we  attempt 
to  solve  their  problems. 

Two  books  *  have  recently  appeared  most  oppor- 
tunely, which  record  the  mature  beliefs  of  two  con- 
spicuous men  of  science  concerning  the  value  and 
necessity  of  scientific  hypothesis.  We  could  scarcely 
have  two  authors  more  widely  contrasted  in  tempera- 
ment and  in  opinions  than  Poincare  and  Sir  Oliver 
Lodge;  the  one,  a  skeptic  who  views  with  detachment 
the  efforts  of  men  to  penetrate  the  mysteries  of  nature, 
and  the  other,  a  credulous  believer  with  equal  convic- 
tion in  matter  and  ether  and  spirits. 

Before  discussing  their  views,  we  should  call  to 
mind  that  Poincare  began  his  career  and  attained  his 
greatest  eminence  as  a  pure  mathematician;  that  he 
later  critically  examined  the  theories  of  physics;  and 
finally  turned  to  philosophy  for  the  purpose  of  examin- 
ing the  foundations  of  science.  Sir  Oliver  Lodge  has 

*  The  Foundations  of  Science.  By  H.  Poincare.  An  author- 
ized translation  by  George  Bruce  Halsted  of  "  Science  and 
Hypothesis,"  "  The  Value  of '  Science,"  and  "  Science  and 
Method,"  with  an  introduction  by  Professor  Royce.  (The 
Science  Press.) 

Continuity.  The  Presidential  Address  to  the  British  Asso- 
ciation for  the  Advancement  of  Science  for  1913.  (Putnam's.) 
By  Sir  Oliver  Lodge. 


194         THE  LIMITATIONS  OF  SCIENCE 

worked  mostly  from  the  experimental  side.  With  an 
early  tendency  toward  speculation,  he  wrote  several 
books  which  aimed  to  give  a  most  concrete,  and  even 
crude,  picture,  of  natural  phenomena.  His  present 
position  as  executive  head  of  a  university  has  thrown 
him  into  the  practical  affairs  of  life.  And  probably 
his  chief  trait  of  mind  is  the  belief  that  all  things,  from 
engines  to  souls,  are  best  considered  as  manifestations 
of  a  luminiferous  ether  which  has  the  characteristics 
of  a  jelly. 

It  will  be  best  now  to  let  Poincare  state  his  ideas 
regarding  the  scientific  method  in  his  own  words :  for 
he  has  done  so  most  lucidly  and  vividly.  The  quota- 
tions are  from  Professor  Halsted's  authorized  trans- 
lations : 

"  Experiment  is  the  sole  source  of  truth.  It  alone 
can  teach  us  anything  new;  it  alone  can  give  us  cer- 
tainty. But  then,  if  experiment  is  everything,  what 
place  will  remain  for  mathematical  physics?  What 
has  experimental  physics  to  do  with  such  an  aid,  one 
which  seems  useless  and  perhaps  even  dangerous  ?  And 
yet  mathematical  physics  exists,  and  has  done  unques- 
tionable service.  We  have  here  a  fact  that  must  be 
explained.  The  explanation  is  that  merely  to  observe 
is  not  enough.  We  must  use  our  observations,  and 
to  do  that  we  must  generalize.  This  is  what  men  have 
always  done;  only  as  the  memory  of  past  errors  has 
made  them  more  and  more  careful,  they  have 


SKEPTICISM  AND  IDOLATRY  195 

observed  more  and  more,  and  generalized  less  and 
less." 

"  It  is  often  said  experiments  must  be  made  without 
a  preconceived  idea.  That  is  impossible.  Not  only 
would  it  make  all  experiment  barren,  but  that  would 
be  attempted  which  could  not  be  done.  Everyone 
carries  in  his  own  mind  his  own  conception  of  the 
world,  of  which  he  cannot  so  easily  rid  himself.  We 
must,  for  instance,  use  language;  and  our  language  is 
made  up  only  of  preconceived  ideas  and  cannot  be 
otherwise.  Only  these  are  unconscious  preconceived 
ideas,  a  thousand  times  more  dangerous  than  the 
others." 

And  he  goes  on  to  show  how  barren  would  be  the 
mere  accumulation  of  experimental  facts,  and  how 
the  master  minds  group  them  into  generalizations  and 
laws  which  make  them  fit  for  use.  Out  of  complexity 
they  achieve  simplicity  and  order.  And  he  warns  us 
that  even  in  this  true  phase  of  science,  lurk  the  dangers 
of  preconceived  ideas,  and  of  inaccuracy  of  expression. 
Having  pointed  out  the  proper  path,  he  then  enters  the 
more  debatable  field  of  hypothesis : 

"  All  generalization,"  he  says,  "  is  a  hypothesis. 
Hypothesis,  then,  has  a  necessary  role  that  no  one  has 
ever  contested.  Only,  it  ought  always,  as  soon  as  pos- 
sible and  as  often  as  possible,  to  be  subjected  to  verifi- 
cation. And  of  course  if  it  does  not  stand  this  test  it 
ought  to  be  abandoned  without  reserve.  This  is  what 


196        THE  LIMITATIONS  OF  SCIENCE 

we  generally  do,  but  sometimes  with  rather  an  ill 
humor." 

"  The  firm  determination  to  submit  to  experiment  is 
not  enough ;  there  are  still  dangerous  hypotheses ;  first, 
and  above  all,  those  which  are  tacit  and  unconscious. 
Since  we  make  them  without  knowing  it,  we  are  power- 
less to  abandon  them.  Here  again,  then,  is  a  service 
that  mathematical  physics  can  render  us.  By  the  pre- 
cision that  is  characteristic  of  it,  it  compels  us  to 
formulate  all  the  hypotheses  that  we  should  make  with- 
out it,  but  unconsciously." 

It  is  just  here  that  I  think  Poincare  begins  to  leave 
sure  ground,  and  by  a  confusion  of  thought  and  terms 
he  falls  into  what  seems  to  me  an  impossible  posi- 
tion. He  first  stated  that  a  generalization  is  an  hypoth- 
esis. It  is  true  that  every  generalization  is  speculative 
to  the  extent  that  we  cannot  verify  it  by  experiment 
with  absolute  accuracy  or  in  all  possible  cases.  For  in- 
stance, no  one  supposes  we  can  ever  record  all  the 
changes  of  energy  which  occur  in  the  universe,  yet  we 
state  with  great  confidence  that  energy  is  conservative. 
The  justification  for  our  belief  is  simple.  All  the 
cases  we  have  measured  confirm  the  law.  And  this 
law  is  of  the  kind  that  can  be  frequently  and  readily 
put  to  the  test  of  experimental  verification;  until 
future  experiments  shall  show  it  to  be  in  error,  we 
have  the  right  to  believe  the  law  correct.  But  hypoth- 
esis has  a  wide  range  of  meanings  besides  that  of 


SKEPTICISM  AND  IDOLATRY  197 

signifying  a  tentative  generalization  which  will  ulti- 
mately be  accepted  as  a  law  or  be  rejected  because  of 
its  increasing  disagreement  with  observations  and,  un- 
fortunately, it  is  used  very  loosely.  It  frequently 
means  those  speculations  in  which  we  indulge  when 
we  attempt  to  define  the  causes  of  phenomena;  when 
we  create  fictitious  substances,  as  an  atom  or  ether; 
and  when  we  construct  models  to  illustrate  the  actions 
of  forces.  None  of  these  cases  is  a  generalization  in 
the  sense  of  Poincare's  first  statement,  because  it  can- 
not be  verified  by  experiment.  It  would  greatly  sim- 
plify thought  if  we  would  confine  the  term  hypothesis 
to  these  speculative  ideas,  and  use  the  words  law  or 
theory  for  those  generalizations  which  are  based  on 
experimental  observations  of  a  material  world.  One 
has  only  to  note  Poincare's  own  confusion  of  thought; 
if  we  must  generalize,  and  if  our  generalizations  are 
hypotheses  which  are  subject  to,  and  must  be  verified 
by,  experiment,  then  such  hypotheses  are  the  truth, 
so  far  as  can  be  determined  by  scientific  methods.  We 
certainly  have  the  right  to  ask :  how  can  they  be  dan- 
gerous and  how  can  there  be  a  too  great  multiplica- 
tion of  them,  if  they  are  the  truth?  If  they  can  be 
subjected  to  experiment,  then  as  soon  as  one  is  dis- 
proved, it  would  necessarily  be  abandoned.  The  reason 
for  his  caution  to  us  is  that  Poincare  knows  that  the 
great  majority  are  incapable  of  verification,  since  they 
deal  with  purely  metaphysical  ideas.  His  own  words, 


198        THE  LIMITATIONS  OF  SCIENCE 

quoted  from  the  introduction  to  his  Theorie  de  la 
Lumiere,  will  prove  this: 

"  It  matters  little  to  us  whether  the  ether  really 
exists;  that  is  the  business  of  the  metaphysician  to 
find  out;  the  essential  thing  for  us  is  that  everything 
acts  as  if  it  existed,  and  that  this  hypothesis  is  con- 
venient in  explaining  phenomena.  After  all,  have  we 
any  other  reason  for  believing  in  the  existence  of  ma- 
terial objects?  Is  not  that  belief  also  a  convenient 
hypothesis ;  only  we  shall  never  cease  to  make  it,  mean- 
while the  time  will  come,  without  doubt,  when  the  ether 
will  be  rejected  as  useless." 

See  what  an  advance  in  confusion  of  thought  we 
have  now!  Hypothesis  is  no  longer  a  necessity,  it  is 
a  convenience.  If  those  of  the  ether  (and  no  idea  has 
been  more  fruitful  than  the  ether)  cannot  be  verified 
by  experiment,  how  can  they  be  convenient,  because  he 
says  unverifiable  hypotheses  are  dangerous;  and  if  they 
can  be  verified,  how  can  we  reject  the  truth,  whether 
they  are  convenient  or  not?  Again,  how  can  every- 
thing act  as  if  the  ether  existed,  unless  it  does  exist? 
Is  not  that  our  definition  of  existence  ?  And  lastly,  one 
would  suppose  that  if  we  shall  never  cease  to  postulate 
the  existence  of  matter,  we  have  come  as  near  making 
matter  a  certainty  as  we  can  ever  attain  to  any  cer- 
tainty. 

The  unfortunate  feature  of  such  statements  is  that 
they  constantly  rise  to  trouble  their  makers.  We  shall 


SKEPTICISM  AND  IDOLATRY  199 

see  later  that  Poincare  absolutely  reverses  this  opinion, 
rejects  matter  and  clings  to  the  ether;  meanwhile,  both 
of  his  opinions  are  unsupported  by  experimental  evi- 
dence, which  he  has  declared  to  be  the  touchstone  of 
truth  and  usefulness  for  hypotheses.  Not  only  does 
Poincare  drift  in  this  hopeless  fashion  between  matter 
and  ether,  but  the  founders  of  the  New  Mechanics  are 
at  sea  as  regards  the  existence  oi  the  ether.  One 
school  of  thought  claims  that  all  substance  is  but  a 
differentiation  of  the  ether,  which  thus  becomes  uni- 
versal substance;  the  other  school  is  just  as  positive  in 
its  belief  that  the  ether  is  a  wornout  fiction.  In  spite 
of  this  trifling  difference  in  their  points  of  view,  both 
schools  arrive  at  much  the  same  conclusions.  At 
least  they  give  us  a  good  illustration  of  the  power  of 
mind  to  modify  matter.  During  the  recent  conference 
at  Brussels  for  the  purpose  of  discussing  the  new  con- 
cepts of  matter  and  mechanics,  Poincare  suggested 
that  it  was  unfortunate  that  physicists  were  using  the 
ether  when  they  needed  it,  and  were  discarding  it  when 
it  proved  troublesome.  Curiously,  no  one  in  the  con- 
ference seemed  to  find  the  situation  of  the  New  Me- 
chanics in  the  least  embarrassing  or  humorous;  the  fact 
is,  the  consequences  announced  at  the  conference  were 
so  unintelligible  that  a  sense  of  humor  would  have 
been  out  of  place. 

Although  Poincare  says  that  we  must  generalize, 
and  that  every  generalization  is  an  hypothesis,  still 


200        THE  LIMITATIONS  OF  SCIENCE 

he  finds  he  must  distinguish  between  different  kinds, 
and  must  warn  us  against  their  indiscriminate  use: 
"  It  is  important  not  to  multiply  hypotheses  beyond 
measure,  and  to  make  them  only  one  after  the  other. 
If  we  construct  a  theory  based  on  a  number  of  hypoth- 
eses, and  if  experiment  condemns  it,  which  of  our 

4? 

premises  is  it  necessary  to  change?  It  will  be  impos- 
sible to  know.  And  inversely,  if  the  experiment 
succeeds,  shall  we  believe  that  we  have  demonstrated 
all  the  hypotheses  at  once  ?  " 

This  is  excellent  advice,  but  when  he  makes  hypoth- 
eses, he  does  not  heed  his  own  warning  and  neither 
does  anyone  else.  Imagine  a  physicist  saying  to 
another,  yours  is  dead,  now  let  me  have  a  turn 
with  one.  But  let  us  follow  Poincare's  classification 
further : 

"  There  are  first  those  which  are  perfectly  natural 
and  from  which  one  can  scarcely  escape.  It  is  diffi- 
cult not  to  suppose  that  the  influence  of  bodies  very 
remote  is  quite  negligible.  .  .  .  They  are  the  last  that 
ought  to  be  abandoned. 

"  There  is  a  second  class  of  hypotheses,  that  I  shall 
term  neutral.  In  most  questions  the  analyst  assumes 
at  the  beginning  of  his  calculations  either  that  matter 
is  continuous  or,  on  the  contrary,  that  it  is  formed  of 
atoms.  He  might  have  made  the  opposite  assumption 
without  changing  his  results.  He  would  only  have 
had  more  trouble  to  obtain  them;  that  is  all.  If,  then, 


SKEPTICISM  AND  IDOLATRY  201 

experiment  confirms  his  conclusions,  will  he  think  that 
he  has  demonstrated,  for  instance,  the  real  existence  of 
atoms?" 

"  These  neutral  hypotheses  are  never  dangerous,  if 
only  their  character  is  not  misunderstood.  They  may 
be  useful,  either  as  devices  for  computation,  or  to  aid 
our  understanding  by  concrete  images,  to  fix  our  ideas 
as  the  saying  is.  There  is,  then,  no  occasion  to  ex- 
clude them. 

"  The  hypotheses  of  the  third  class  are  the  real  gen- 
eralizations. They  are  the  ones  that  experiment  must 
confirm  or  invalidate.  Whether  verified  or  condemned, 
they  will  always  be  fruitful.  But  for  the  reasons  that 
I  have  set  forth,  they  will  only  be  fruitful  if  they  are 
not  too  numerous." 

It  would  seem  to  almost  anyone  that  the  first  and 
third  classes  are  so  different  from  the  second  class, 
that  it  is  advisable  to  call  them  laws,  and  limit  the 
term  hypothesis  to  the  speculative  second  class.  The 
class  of  neutral  hypotheses  is  evidently  the  melting-pot 
for  the  bewildering  ethers,  atoms,  subtile  fluids  which 
abound  in  the  physical  sciences,  and  which  have  their 
analogues  in  all  the  others.  Poincare  teaches  us  that 
we  shall  never  acquire  any  definite  knowledge  from 
them,  and  then  he  makes  the  amazing  statement  that 
there  is  no  need  to  exclude  them  if  they  are  not  mul- 
tiplied, if  they  are  made  one  after  the  other,  and  if 
their  character  is  not  misunderstood.  Anyone  in  the 


202        THE  LIMITATIONS  OF  SCIENCE 

least  conversant  with  their  history  knows  that  their 
number  is  great,  and  that  they  are  not  proposed  con- 
secutively. As  for  their  character,  he  evidently  means 
that  they  are  dangerous  if  we  forget  they  are  mere 
conveniences,  fictions,  not  to  be  taken  too  seriously.  It 
is  perfectly  safe  to  say  that  there  is  scarcely  a  text- 
book or  a  treatise  in  any  science  which  does  not  state 
explicitly  that  the  sort  of  things  classed  by  Poincare 
as  neutral  hypotheses,  are  realities  and  not  conjectures. 
Before  showing  how  Poincare  and  Sir  Oliver  Lodge 
confirm  this  opinion,  let  me  quote  two  statements  of 
Sir  J.  J.  Thomson: 

"  The  ether  is  not  a  fantastic  creation  of  the  specu- 
lative philosopher ;  it  is  as  essential  to  us  as  the  air  we 
breathe.  .  .  .  The  study  of  this  all-pervading  sub- 
stance is  perhaps  the  most  fascinating  and  important 
duty  of  the  physicist." 

"  The  possession  of  a  charge  by  the  ions  increases 
so  much  the  ease  with  which  they  can  be  traced  and 
their  properties  studied  that,  as  the  reader  will  see,  we 
know  far  more  about  the  ion  than  we  do  about  the  un- 
charged molecule." 

Evidently  convenience  of  computation  and  an  aid  to 
our  understanding  by  concrete  images  are  not  at  all  in 
the  minds  of  even  eminent  physicists  when  they  indulge 
in  neutral  hypotheses  of  ethers  and  atoms. 

Now  let  us  return  to  Poincare,  and  see  how  he  heeds 
his  own  warning.  But  first  notice  how  clear  and  how 


SKEPTICISM  AND  IDOLATRY  203 

vivid  his  thought  is  when  he  is  not  involved  in  these 
pitfalls  to  accurate  reasoning :  "  Is  not  each  great  ad- 
vance accomplished  precisely  the  day  someone  has 
discovered  under  the  complex  aggregate  shown  by  our 
senses  something  far  more  simple,  not  even  resembling 
it — as  when  Newton  replaced  Kepler's  three  laws  by 
the  simple  law  of  gravitation,  which  was  something 
simpler,  equivalent,  yet  unlike  ?" 

To  this  excellent  question,  he  gives  the  following 
lamentable  answer : 

"  One  is  justified  in  asking  if  we  are  not  on  the  eve 
of  just  such  a  revolution  or  one  even  more  important. 
Matter  seems  on  the  point  of  losing  its  mass,  its  solid- 
est  attribute,  and  resolving  itself  into  electrons.  Me- 
chanics must  then  give  place  to  a  broader  conception 
which  will  explain  it,  but  which  it  will  not  explain.  .  .  . 
The  ether  it  is,  the  unknown,  which  explains  matter, 
the  known;  matter  is  incapable  of  explaining  the 
ether." 

How  can  Poincare  justify  himself?  When  we  re- 
call how  Newton  refrained  from  giving  any  hypoth- 
esis regarding  the  cause  or  nature  of  gravitational 
force,  because  he  felt  such  an  hypothesis  would  be  out- 
side the  field  of  science;  and  how  the  subsequent  veri- 
fication of  the  law  of  gravitation  by  innumerable 
experimental  observations  has  established  it  as  one  of 
the  few  great  and  universal  laws;  and  when  we  recall 
what  Poincare  says  about  electrons,  the  ether,  and 


204        THE  LIMITATIONS  OF  SCIENCE 

neutral  hypotheses  in  general,  how  can  we  be  expected 
to  see  any  similarity  in  these  two  revolutions?  The 
two,  on  the  contrary,  are  diametrically  opposed  to 
each  other.  Does  Poincare  really  mean  that  it  is  to  be 
the  function  of  science  to  resolve  matter,  which  he 
said  we  must  always  assume  to  be  an  objective  reality 
whether  we  can  prove  it  or  not,  into  electrons,  an 
hypothetical  component  of  the  hypothetical  atom,  the 
assumption  of  whose  reality  should  be  a  mere  fugitive 
matter  of  convenience?  And  does  he  believe  the  boast 
of  science,  that  it  shall  rest  on  the  objective  experi- 
ence of  our  sensations  rather  than  on  the  subjective 
proof  of  our  imaginations,  can  be  maintained,  if  we 
admit  for  an  axiom,  that  henceforth  it  shall  be  the 
aim  of  science  to  explain  the  known  by  the  unknown  ? 
He  might  have  pursued  this  revolution  further;  the 
dissolution  of  matter  into  the  electron  is  but  the  first 
step  in  the  confusion  of  ideas,  those  who  are  promoting 
it  are  further  transforming  the  electron  into  a  strain 
in  the  ether  of  a  type  unknown  to  experience,  and  the 
most  advanced  are  dissolving  the  ether  into  nothing. 
The  process  of  explaining  the  known  by  the  unknown 
is  complete ;  matter  to  atoms ;  atoms  to  electrons ;  elec- 
trons to  ether;  ether  to  nothing.  Truly,  philosophy 
and  theology  are  gross  materialism  compared  with 
such  a  science.  Can  he  so  quickly  and  completely  for- 
get his  wholesome,  skeptical,  and  critical  attitude, 
merely  because  he  also  is  tempted  to"  indulge  in  specu- 


SKEPTICISM  AND  IDOLATRY  205 

lation?  As  an  example  of  what  absurdities  are  ad- 
vanced in  speculative  physics,  I  give  his  final  utterance 
on  the  existence  and  nature  of  matter,  which  he  de- 
livered in  a  lecture  on  the  "  New  Mechanics  " :  "  We 
can  almost  say  that  there  is  no  longer  matter,  but  only 
holes  in  the  ether ;  and  in  so  far  as  these  holes  seem  to 
play  an  active  part,  it  consists  in  the  inability  of  these 
holes  to  change  their  location  without  influencing  the 
surrounding  ether  which  exerts  a  reactive  influence  on 
such  changes." 

What  to  make  of  such  a  statement  passes  under- 
standing. There  was  once  a  man  who  pestered  the 
students  in  Baltimore  by  giving  them  tracts  which 
proved  in  fifty-seven  or  more  different  ways  that  the 
earth  was  hollow,  and  that  we  lived  on  the  inside,  and 
so  in  a  hole.  But  not  even  he  was  so  confused  as  to 
contend  that  we  were  holes  living  on  the  outside  of  a 
hole.  Poincare  has,  of  course,  no  resemblance  to  that 
man  and  yet,  unless  he  means  something  by  the  word 
"  hole  "  which  is  understood  exclusively  by  himself  and 
a  small  coterie  of  physicists  who  write  in  the  same 
absurd  fashion,  there  is  no  more  sense  in  his  definition 
of  matter.  If  there  were  any  connection  between 
the  words  and  the  idea — that  is,  if  he  were  trying  to 
define  the  word  matter  so  as  to  express  our  experience 
of  it,  then  his  statement  makes  matter  the  answer  to 
the  old  conundrum :  "  What  is  it,  the  more  you  take 
from  it,  the  more  it  be?  "  I  admit  matter  is  not  ether ; 


206        THE  LIMITATIONS  OF  SCIENCE 

but  if  it  is  a  hole,  then  a  hole  in  the  ether  is  just  the 
contrary  to  a  hole.  Holes  never  even  seem  to  play  an 
active  part  in  anything;  they  show  no  inclination  or 
ability  of  themselves  to  change  their  location;  and 
nothing,  except  an  ether,  has  ever  been  conceived  of  as 
able  to  react  on  a  hole.  The  simple  fact  of  the  case 
is,  such  statements  are  attempts  to  do  just  what  Poin- 
care  said  they  were, — attempts  to  explain  the  known  by 
the  unknown.  The  pity  of  it  is  that  science  is  filled 
with  just  such  attempts ;  we  recognize  the  words  used, 
but  their  sense  is  so  twisted  that  they  really  express 
no  clear  idea.  In  comparison  with  such  quibbles  and 
such  verbal  distortion,  the  action  of  Dr.  Johnson, 
when,  in  answer  to  the  similar  logic  of  a  metaphysician 
of  the  Berkeleian  type,  he  kicked  a  stone  as  our  ulti- 
mate proof  of  the  existence  of  matter,  is  true  science — 
at  least  it  is  organized  common  sense.  It  is  comical 
to  read  the  opinions,  concerning  the  essence  of  matter, 
of  those  modern  physicists  who  have  succumbed  to  the 
fascination  of  explaining  the  known  by  the  unknown. 
Led  by  a  small  band  of  German  physicists,  they  use 
mathematical  symbols  and  scientific  phrases;  and  yet 
they  are  explaining  phenomena  in  quite  the  approved 
medieval  fashion  of  transcendental  symbolism.  It  is 
perfectly  easy  to  match  their  statements  with  the  ab- 
stract theorems  of  an  Albert  Magnus  or  a  St.  Thomas 
Aquinas.  In  other  words,  modern  science  has  sud- 
denly taken  a  leap  into  pure  metaphysics,  while,  at  the 


SKEPTICISM  AND  IDOLATRY  207 

same  time,  it  persists  in  the  habit  of  sneering  at  meta- 
physical methods. 

It  was  with  the  greatest  regret  that  I  found  Poincare 
had  given  in  to  this  form  of  idolatry  of  the  graven 
images  of  science.  His  mathematical  writings,  his 
physical  theories,  and  his  critical  spirit  had  always 
impressed  me  as  models  of  clear  and  vivid  thinking. 
And  the  statements  I  have  quoted  show  that  he  did  not 
adopt  this  other  mode  of  messy  thinking  without 
reluctance.  His  ideas  no  longer  are  unqualified:  he 
is  willing  to  admit  only  that  things  seem  to  point  this 
way  or  that,  as  if  he  had  been  caught  and  entangled  in 
this  German  school  of  transcendental  symbolism,  and 
could  not  see  his  way  out. 

Sir  Oliver  Lodge  has  no  such  scruples.  He  rejoices 
in  his  beliefs,  and  delights  in  promulgating  a  clear 
knowledge  of  all  the  unknowable  things  in  the  universe 
just  as  he  sees  them ;  especially  by  popular  essays  ad- 
dressed to  those  whose  lack  of  technical  training  makes 
them  unable  to  discriminate  between  real  and  sham 
science.  In  his  recent  presidential  address  on  "  Con- 
tinuity," he  tries  to  accept  at  once  the  modern  me- 
chanics and  Newtonian  mechanics,  continuity  and  dis- 
continuity, and  scientific  laws  for  bodies  both  mortal 
and  immortal.  But  with  all  the  trouble  which  this 
reconciling  of  irreconcilables  gives  him,  he  always 
finds  comfort  and  refreshment  in  his  "  fervent  belief  in 


208         THE  LIMITATIONS  OF  SCIENCE 

the  Ether  " :  in  some  way  it  will  solve  our  difficulties. 
This  is  his  creed: 

"  The  Ether  is  the  universal  connecting  medium 
which  binds  the  universe  together,  and  makes  it  a  co- 
herent whole  [not  hole]  instead  of  a  chaotic  collection 
of  independent  isolated  fragments.  It  is  the  vehicle 
of  transmission  of  all  manner  of  force,  from  gravita- 
tion down  to  cohesion  and  chemical  affinity ;  it  is  there- 
fore the  store-house  of  potential." 

In  short,  the  Ether,  not  being  matter,  is  for  Sir 
Oliver  pretty  nearly  everything  else;  almost,  if  not 
quite,  God,  even  to  the  use  of  the  reverential  capital 
initial.  More  specifically,  he  considers  it  the  principle 
of  continuity,  and  in  continuity  he  finds  a  scientific 
proof  of  immortality.  If  he  had  based  a  belief  in  the 
immortality  of  the  soul  on  an  analogy  with  the  con- 
tinuity of  existence  of  matter  and  energy,  I  think  many 
persons  would  agree  that  he  was  expressing  one  of  our 
most  certain  reasons  for  such  a  hope.  It  is  difficult 
to  suppose  that  the  quantity  of  matter  and  energy  in 
the  universe  is  unchangeable,  and  yet  to  maintain  that 
thought  and  emotion,  which  have  so  many  of  the  char- 
acteristics of  durability,  end  with  death.  On  the  con- 
trary, "  we  *  do  see  the  sum  of  mind  increasing  every 
time  two  old  thoughts  coalesce  into  a  new  one,  or  even 
every  time  matter  assumes  a  new  form  before  a  re- 
ceiving intelligence."  But  such  an  intimation  of  im- 
*  Unpopular  Review,  April,  1914. 


SKEPTICISM  AND  IDOLATRY  209 

mortality  is  a  very  different  thing  from  assuming  a 
body  of  postulates  and  creating  a  de  facto  science  of 
psychic  phenomena,  as  Sir  Oliver  Lodge  does.  Science 
must  deal  with  material  things,  and  must  be  confined  to 
our  sense  perceptions.  So  that,  whether  immortality 
and  psychic  phenomena  be  ultimately  accepted  or  not, 
the  proof  must  be  expected  by  other  than  scientific 
methods,  unless  we  give  to  these  words  a  totally  dif- 
ferent significance  from  what  they  had  in  the  past. 
Omitting  all  other  difficulties,  one  wonders  how  imma- 
terial intelligences  can  make  material  noises,  for,  if 
they  do,  what  becomes  of  our  law  of  conservation  of 
energy  which  accounts  for  all  material  motion  by  ma- 
terial causes?  Of  course  he  falls  back  on  his  omnipo- 
tent Ether : 

"  The  evidence  to  my  mind  goes  to  prove  that  dis- 
carnate  intelligences,  under  certain  conditions,  may 
interact  with  us  on  the  material  side,  thus  indirectly 
coming  within  our  scientific  ken;  and  that  gradually 
we  may  hope  to  attain  some  understanding  of  the 
nature  of  a  larger,  perhaps  ethereal,  existence,  and  of 
the  conditions  regulating  intercourse  across  the  chasm." 

Science  is  still  burdened  with  the  inexplicable  mys- 
tery of  the  material  world,  and  it  should  not  open  the 
doors  of  its  temple  for  the  worship  of  graven  images, 
even  if  the  idol  is  the  great  god  Ether.  Sir  Oliver 
Lodge's  speculations  are  not  even  qualified  by  logical 
methods.  His  reasoning  is  apparently  a  mere  play  on 


210         THE  LIMITATIONS  OF  SCIENCE 

words:  Immaterial  spirits  are  not  material  bodies,  the 
ether  is  not  matter;  therefore  spirits  may  be  ethereal 
bodies.  It  does  considerable  harm  when  he  uses  his 
official  position  and,  as  it  were,  makes  the  British  As- 
sociation indorse  such  foolish  views. 

Sir  Oliver  Lodge  still  believes  with  the  past  genera- 
tion of  physicists  that  science  has  discovered  a  path 
to  positive  knowledge :  "  Many  scientific  men,'5  he  says, 
"  still  feel  in  pugnacious  mood  towards  Theology,  be- 
cause of  the  exaggerated  dogmatism  which  our  prede- 
cessors encountered  and  overcame  in  the  past.  They 
had  to  struggle  for  freedom  to  find  truth  in  their  own 
way;  but  the  struggle  was  a  deplorable  necessity,  and 
has  left  some  evil  effects."  It  has  left  evil  effects,  and 
the  chief  of  them  is  Scientific  Dogmatism. 

In  spite  of  our  self-confidence,  we  cannot  be  too 
sure  that  hypothetical  science  has  not  traversed  the 
same  path  as  dogmatic  theology.  We  have  a  fairly 
large  and  clearly  defined  body  of  moral  facts.  And 
we  have  generalized  from  them  rather  consistent  moral 
laws.  It  is  inevitable  that  we  shall  always  speculate  as 
to  the  causes  of  these  moral  facts  and  laws,  and  it  is 
probable  that  most  men  will  continue  to  fashion  an 
image  of  their  idea  of  God,  more  or  less  anthropo- 
morphic and  concrete.  But  unfortunately  for  religion, 
many  will  not  stop  at  this  point  of  pure  speculation,  or 
the  worship  of  God  in  spirit  and  in  truth,  but  they  will 
carve  for  themselves  images  in  wood  and  stone,  and 


SKEPTICISM  AND  IDOLATRY  211 

bow  down  and  worship  these  images  as  realities.  So 
also  there  are  the  many  who  will  not  stop  at  the  great 
and  scientific  work  of  discovering  phenomena  and 
laws,  but  they  will  speculate  on  natural  causes  and 
mechanisms.  If  they  do  this  with  an  open  mind,  per- 
haps no  harm  is  done  as  Poincare  says,  and  possibly  the 
imagination  may  be  healthfully  stimulated.  How  few 
stop  at  this  point  may  be  imagined  from  the  examples 
I  have  given ;  a  large  and  increasing  number  have  be- 
come idolaters,  and  are  worshiping  the  graven  images 
of  science  with  dogmatic  fervor. 


CHAPTER  VII 
SCIENCE  AS  THE  ARBITER  OF  ETHICS 

Sire,  in  this  system  there  is  no  need  of  a  God.— LAPLACE. 

WHEN  Renan  wrote  that  humanity  must,  in  future, 
look  to  science  for  what  it  craves  in  the  way  of  a  law 
and  symbol,  science  was  in  the  full  swing  of  conquest. 
The  war  between  it  and  religion  was  believed  to  be  all 
but  over.  The  law  of  evolution  was  accepted  not  only 
in  its  general  aspects,  but  also  it  was  believed  that  in 
natural  selection  a  cause  had  been  discovered  which 
would  permit  us  to  trace  the  progress  of  the  organic 
world  from  the  simple  protoplasm  to  the  most  complex 
forms  of  life.  Search  was  made  for  the  missing  link 
between  man  and  the  lower  animals,  and  those  at- 
tributes which  an  earlier  age  was  content  to  group  as 
spiritual  powers  were  abolished  as  unscientific.  It  was 
inevitable  that  philosophers  like  Renan  and  Spencer 
would  propose  an  evolutionary  law  for  society,  and 
that  even  religion  would  fall  in  line  and  make  of  God  a 
sort  of  omnipotent  and  beneficent  natural  force  which 
gently  led  man  up  to  ever  higher  types  of  perfection. 

And  while  to-day  those  who  cultivate  the  more  exact 
sciences  have  come  to  believe  that  the  objective  and 


212 


THE  ARBITER  OF  ETHICS  213 

subjective  worlds  are  governed  by  different  forces,  the 
wave  of  evolutionary  philosophy,  under  scientific  domi- 
nation, has  spread  to  the  students  of  political  and 
social  history  who  are  trying  to  devise  a  state  which 
shall  evolve  toward  better  conditions  by  natural  means. 
The  result  is  that  the  attitude  of  thoughtful  people 
toward  the  moral  questions  of  the  day  is  one  of  more 
or  less  perplexity.  Few  of  them  are  willing  to  accept 
the  doctrine  that  human  nature  is  essentially  good  and 
that  the  only  need  of  society  is  to  remove  all  restraint. 
In  the  past,  the  majority  of  men  experienced  this  neces- 
sary restraint  in  the  conviction  of  personal  respon- 
sibility to  a  God,  who  actively  interfered  in  their 
thoughts  and  deeds,  and  who  rewarded  or  punished 
according  to  a  revealed  standard  of  righteousness. 
But  with  the  growth  of  knowledge  and  especially  with 
the  impersonal  attitude  assumed  in  scientific  inquiry, 
the  impression  has  become  widespread  that  mankind 
has  been  left  to  work  out  its  own  destiny.  So,  as  I 
have  said,  thoughtful  people  are  perplexed  to  know 
where  to  turn  to  find  an  inner  check  which  can  replace 
that  sense  of  personal  responsibility  to  a  God  which, 
however  men  might  rebel,  did  exert  a  steady  and  po- 
tent influence  upon  them.  Some  still  cling  to  the  idea 
that  the  Christian  church  will  ultimately  discover  again 
the  guiding  principle  for  society;  that  a  new  reforma- 
tion from  within  is  all  that  is  necessary.  But  the  diffi- 
culty is  graver  than  in  the  past,  as  such  reformations 


214         THE  LIMITATIONS  OF  SCIENCE 

involved  matters  of  doctrine  rather  than  a  change  in 
fundamental  ideas.  Many  are  simply  drifting;  but 
an  increasingly  large  number  are  frankly  turning  to 
scientific  doctrines  in  the  hope  that  a  deeper  experi- 
mental knowledge  of  the  laws  of  man's  individuality, 
of  his  social  relations,  and  of  his  environment  will 
bring  with  it  the  solution  of  the  problem.  And  in 
spite  of  our  very  deficient  acquaintance  with  such  laws, 
some  are  proclaiming  that  this  naturalism  is  the 
surest  guide  for  us  in  evolving  a  society  nearer  to  the 
ideally  good.  Apparently,  they  have  the  idea  that 
accurate  observations  and  statistical  records,  which 
may  be  formulated  into  scientific  laws,  are  sufficient 
as  guides  to  conduct. 

A  curious  feature  of  the  discussions,  which  have 
arisen  about  these  new  systems  of  scientific  ethics,  is 
that  almost  no  attention  is  paid  to  the  fundamental 
question  whether  the  deductions  of  science  are  suitable 
to  serve  as  an  ethical  principle  for  society;  or  even 
whether  science,  except  indirectly,  concerns  itself  with 
character;  yet  character,  or  the  judging  between  right 
and  wrong,  is  necessarily  the  essence  of  all  systems  of 
ethics.  Now  I  think  it  can  be  shown  that  the  pursuit 
of  science  has  for  its  aim  to  acquire  power;  that  is,  we 
seek  through  science  to  learn  the  facts  of  nature  and  to 
interfere  with  natural  forces  so  as  to  make  them  serve 
man's  desires.  As  an  illustration  of  the  mixture  of 
truth  and  fallacy,  which  is  typical  of  many  who  advo- 


THE  ARBITER  OF  ETHICS  215 

cate  scientific  ethics,  consider  this  statement  of  a  writer 
on  genetics  which  merely  reflects  a  widespread  opinion : 
"  Human  civilization  goes  hand  in  hand  with  the  de- 
gree of  successful  interference  which  man  exerts  upon 
the  natural  forces  surrounding  him."  The  truth  of 
this  statement  lies  in  the  correct  view  that  the  pur- 
pose of  scientific  inquiry  is  not  only  to  discover  the 
forces  of  nature  but  to  interfere  with  them  so  as  to 
increase  man's  dominating  power;  the  falsehood  con- 
sists in  assuming  that  civilization  is  based  on,  or  even 
necessarily  runs  with  power.  Everyone  knows  that 
power  may  make  for  evil  as  efficiently  as  for  good; 
the  ethical  standard  of  a  civilization  depends  on  the 
will  of  its  individuals  to  choose  between  right  and 
wrong.  To  deny  this,  is  to  refuse  the  attributes  of 
the  noblest  civilization  to  Jesus,  to  Buddha,  to  Socrates, 
each  of  whom  was  quite  ignorant  of  science,  and  lived 
in  times  when  men  exerted  themselves  but  little  to 
interfere  with  natural  forces.  Nor  could  we  to-day,  in 
the  midst  of  an  earnest  scientific  endeavor,  deny  that  a 
civilization  higher  than  our  own  would  be  possessed 
by  a  community  formed  of  men  like  to  them. 

The  greatest  difficulty  encountered,  if  the  attempt  be 
made  to  determine  the  ethical  value  of  science,  is,  as  I 
have  said  before,  the  lack  of  a  spirit  of  serious  criti- 
cism amongst  men  of  science,  with  the  consequent 
absence  of  critical  data  on  the  aims  of  science  and  on 
the  effect  which  scientific  activity  has  had  on  society. 


216        THE  LIMITATIONS  OF  SCIENCE 

Before  much  can  be  done  to  find  out  what  the  influ- 
ence of  science  on  morals  has  been,  a  school  of  critics 
of  men  of  science  must  be  created.  I  am  quite  aware 
that  this  opinion  is  counter  to  the  general  belief  that 
science  is  the  most  critical  of  all  human  endeavor.  The 
results  of  experimental  investigation  and  the  mathe- 
matical laws  formulated  from  them  seem  so  positive, 
so  subject  to  minute  and  patient  scrutiny,  that  it  may 
well  seem  that  men  of  science  are  critical.  But  this 
form  of  criticism  is  limited  to  the  mere  question  of 
accuracy  of  observation  and  logic.  Before  the  sub- 
jective influence  of  science  on  character  can  be  deter- 
mined, the  postulates  of  science  and  the  scientific 
method  itself  must  be  outlined  clearly  and  discussed 
critically;  it  is  this  higher  criticism  which  is  lacking 
in  men  of  science. 

If  such  a  body  of  criticism  existed  it  is  probable 
that  a  philosophy  of  science  could  be  created.  But  the 
present  method  of  educating  men  to  engage  in  scientific 
work  is  little  likely  to  foster  the  critical  or  even  the  his- 
torical attitude.  In  fact,  most  men  of  science  know 
so  little  of  metaphysics  or  even  of  the  historical  de- 
velopment of  science  that  they  are  quite  ignorant  of 
how  metaphysical  their  sciences  are.  If  they  were 
conversant  with  the  history  of  scientific  thought,  they 
would  see  that  while  scientific  laws  are  as  positive  and 
as  objective  as  human  knowledge  has  been  able  to 
attain,  yet  the  hypotheses  of  science,  which  aim  to  dis- 


THE  ARBITER  OF  ETHICS  217 

cover  the  causes  of  phenomena  and  to  simulate  the 
mechanism  of  natural  forces,  are  as  subjective  and  as 
dependent  on  human  opinion  as  any  other  form  of 
knowledge.  And  it  is  just  these  subjective  and  meta- 
physical aspects  of  science  which  are  concerned  in  the 
question  of  the  relation  of  the  external  world  of 
phenomena  to  our  internal  world  of  ideas. 

One  would  naturally  turn  to  the  histories  of  science, 
not  only  for  the  data  of  scientific  experience,  but  also 
for  that  larger  aspect  of  the  question,  the  discussion 
of  the  relations  between  scientific  thought  and  other 
forms  of  human  activity.  But  almost  without  excep- 
tion our  histories  of  science  are  mere  chronicles  of 
scientific  experiments  and  hypotheses.  The  work  of 
each  man  of  science  is  outlined  in  as  great  detail  as  the 
scope  of  the  history  permits,  as  if  everything  done  in 
the  name  of  science  were  important.  What  we  should 
have,  is  a  discussion  of  the  development  of  the  sub- 
ject and  of  the  relations  between  the  intellectual  forces 
of  a  given  epoch  and  the  scientific  activity  of  the  same 
period ;  for  example,  there  should  be  shown  the  relation 
of  the  ideas  of  Galileo,  Copernicus,  and  Descartes  to 
the  Renaissance ;  at  a  later  date  there  is  a  similar  close 
connection  between  the  rise  of  electricity,  the  skeptical 
spirit  of  the  mathematical  physicists,  and  the  revolu- 
tionary and  democratic  ideas  which  were  prevalent  at 
the  beginning  of  the  nineteenth  century. 

The  most  striking  evidence  of  the  ineffectiveness 


218        THE  LIMITATIONS  OF  SCIENCE 

of  scientific  histories  is,  however,  their  attitude  toward 
hypothesis.  Such  hypotheses  are  clearly  subjective  in 
character  and  are  to  be  criticised  in  accordance  with 
the  same  standards  as  a  philosophical  system  of  Plato 
or  Kant.  Instead  of  this  they  are  invariably  treated  as 
if  they  dealt  with  phenomena  verifiable  by  experi- 
ment. 

In  our  histories  of  science  a  number  of  things  about 
scientific  hypotheses  might  have  been  brought  out.  In 
the  first  place,  all  of  them  rest  on  mechanical  analogies 
and  attempt  to  make  of  the  world,  both  inorganic  and 
organic,  a  vast  machine  whose  parts  grind  out  motions 
which  reveal  themselves  to  us  as  heat,  light,  thought, 
and  whatever  else  we  are  cognizant  of.  That  is,  a 
mechanical  explanation  of  phenomena  is  considered  to 
be  the  simplest  and  most  satisfactory  one  that  can  be 
given.  But  we  know  there  is  no  criterion  which  will 
distinguish  the  truth  between  many  rival  mechanical 
hypotheses.  Thus  the  explanation  of  phenomena  is 
dependent  on  subjective  interpretation,  and  is  in  the 
end  a  matter  of  personal  opinion.  Nor  does  the  recent 
attempt  to  replace  matter  by  electricity  escape  this 
difficulty  since  the  principles  governing  electrical 
forces  and  energy  are  the  same  as  those  controlling 
matter.  The  restrictions  pointed  out  are  still  in  force, 
with  the  substitution  of  the  word  electricity  for  matter. 

It  is  also  evident  that,  however  logically  a  scientific 
hypothesis  may  be  developed,  we  can  never  say  that 


THE  ARBITER  OF  ETHICS 

it  is  anything  more  than  our  idea  of  the  world;  thus 
scientific  hypothesis  stands  on  the  same  ground  as  any 
other  kind  of  logical  thought.  Criticism  of  hypotheses 
should  therefore  be  directed  principally  to  their  postu- 
lates. 

In  the  next  place,  the  postulates  of  science  are  al- 
ways metaphysical  in  character  since  we  must  assume 
initial  conditions  of  space,  time,  and  substance  which 
are  not  subject  to  experimental  verification  and  which 
are  contradictory  to  our  experience  of  the  present 
state  of  those  quantities. 

We  imagine  a  simple  primordial  universe  which  is 
crudely  fictitious,  and  start  it  going  on  its  complicated 
career  by  the  action  of  some  universal  force  which  un- 
balances and  unlocks  its  internal  actions  and  reac- 
tions. 

Then  we  assume  the  existence  of  fictitious  sub- 
stances, atoms,  which  we  deliberately  fashion  so  small 
as  to  be  below  the  limit  of  observation.  We  endue 
them  with  as  many  different  and  contradictory  at- 
tributes as  may  suit  our  convenience  in  order  to 
fashion  the  diverse  forms  of  bodies  by  their  combina- 
tion. 

And  lastly,  if  we  are  to  attempt  to  include  in  the 
name  of  science  all  laws,  we  must  provide  portions  of 
this  machine  with  life,  thought,  and  self -consciousness 
as  a  form  of  mechanical  forces. 

Evidently,  the  postulates  of  science  are  as  complex, 


220        THE  LIMITATIONS  OF  SCIENCE 

as  subjective,  and  as  debatable  as  the  postulates  of 
religion  and  philosophy.  And  they  also  lack  the  sim- 
plicity and  generality  which  have  made  the  postulates 
of  geometry  universally  acceptable  and  have  given  to 
them  the  appearance  of  finality.  And  from  these  meta- 
physical postulates  of  natural  science,  the  scientific 
conclusions  follow  which  somehow  impress  us  as  being 
positive  knowledge  not  subject  to  human  opinion. 

Since  most  of  our  scientific  postulates  and  the 
hypotheses  which  are  developed  from  them  are  not 
questions  of  objective  facts,  they  must  have  an  influ- 
ence which  may  be  helpful,  harmful,  or  indifferent. 
And  it  should  be  the  chief  duty  of  the  historian  and 
the  critic  to  trace  this  influence.  Instead  of  this 
critical  spirit,  it  is  only  too  common  for  men  of  science 
to  insist  that  all  hypotheses  are  meritorious.  This 
opinion  is  so  widespread,  that  it  is  frequently  stated 
that  even  if  a  hypothesis  be  entirely  false,  yet  it  may 
be  useful.  The  reason  for  this  lack  of  discrimination 
lies  probably  in  the  fact  that  science  has  gradually 
created  two  worlds  connected  by  only  a  slender  thread ; 
one  the  experimental  world  of  our  sensations,  and  the 
other  a  fictitious  world  of  our  imagination.  What- 
ever the  prevailing  hypothesis  may  be,  the  experi- 
mentalist continues  his  work,  confident  in  the  belief 
that  if  his  results  agree  with  a  hypothesis  they  will  be 
taken  as  a  confirmation  of  it;  and  if  they  disagree,  then 
he  may  be  sure  that  the  hypothesis  will  be  modified  so 


THE  ARBITER  OF  ETHICS  221 

as  to  conform  to  them.  Thus  the  phenomena  and  laws 
of  light  continue  to  unfold  themselves  in  a  consistent 
progress  in  spite  of  the  fact  that  now  one,  and  now 
another,  contradictory  hypothesis  of  the  mechanism  of 
light  and  its  transmission  through  space  is  uppermost. 
This  is  the  explanation  of  the  reason,  so  puzzling  to 
the  layman,  why  two  conflicting  hypotheses,  explaining 
the  same  class  of  phenomena,  can  be  maintained  and 
cultivated  at  the  same  time.  There  is  no  telling  when 
new  facts  will  be  discovered  which  will  bring  an  al- 
most discarded  hypothesis  back  into  favor.  The  fic- 
titious worlds  of  natural  science  bear  a  close  analogy 
to  those  hypergeometrical  realms  of  the  mathematician 
which,  while  logical  and  interesting,  do  not  rest  on 
experience  and  so  do  not  exist.  Such  mathematical 
worlds  of  the  imagination  are  invented  as  a  sort  of 
intellectual  game  and  can  -have  no  influence  on  human 
actions  and  society;  so  also  the  hypothetical  properties 
ascribed  to  nature  by  the  physicist  cannot  affect  our 
relations  to  our  environment. 

This  neglect  of  the  critical  field  by  men  of  science 
has  resulted  in  leaving  to  metaphysicians  the  discus- 
sion of  scientific  methods  and  the  development  of  what 
now  passes  under  the  name  of  scientific  philosophy. 
Whatever  the  influence  of  this  criticism  may  have  been 
on  philosophy  and  on  thought  generally,  it  is  safe  to 
say  that  it  has  had  little  on  science;  its  conclusions 
have  not  engaged  the  attention  of  men  of  science  very 


222         THE  LIMITATIONS  OF  SCIENCE 

seriously.  The  reason  for  their  indifference  is  two- 
fold. Rightly  or  wrongly,  it  is  felt  that  the  meta- 
physicists  are  too  engrossed  in  the  exact  definitions  of 
terms  and  in  the  niceties  of  verbal  expression.  They 
thus  miss  or  confuse  the  real  issue  of  science,  which  is 
to  discover  the  significance  and  influence  of  objective 
facts  rather  than  of  words.  This  does  not  mean  that 
the  careful  use  of  words  is  not  important  in  science. 
It  is  only  too  apparent  that  many  of  the  battles  of 
science  are  waged  over  the  meaning  of  words  and  not 
of  phenomena. 

The  other  reason  for  the  ineffectiveness  of  this  sci- 
entific philosophy  as  developed  by  the  metaphysicists 
is  that  they  are  not  disciplined  by  labor  in  the  labora- 
tory nor  trained  in  the  analysis  and  technique  of 
scientific  theory.  They  must  thus  depend  on  elemen- 
tary treatises,  which  are  rarely  the  work  of  master 
minds;  or  they  can  approach  the  great  thinkers  only 
through  the  medium  of  popular  expositions  in  which 
the  most  scrupulous  are  somewhat  relaxed.  To  con- 
trast the  opinions  of  Plato  with  Ganot  does  not  com- 
mand respect ;  and  to  depend  on  the  popular  addresses 
of  a  Helmholtz  or  a  Lord  Kelvin  is  not  to  know  their 
real  thought.  The  first  leads  to  frequent  errors  and 
the  second  to  sweeping  conclusions.  If  we  are  to 
develop  a  satisfactory  scientific  philosophy  it  seems 
requisite  to  have  it  done  by  men  trained  in  science  and 
conversant  with  philosophy ;  this  combination  has  been 


THE  ARBITER  OF  ETHICS  223 

a  rare  one,  of  which  the  greatest  examples  are  Aris- 
totle, Descartes,  and  possibly  Kant. 

It  is  difficult  to  see  how  this  combination  of  science 
and  philosophy  is  to  be  obtained  with  the  present  sys- 
tem of  training  men  in  our  graduate  schools.  The 
prospective  man  of  science  is  taught  laboratory  methods 
and  becomes,  thanks  to  it  and  to  his  research  work,  a 
rather  skillful  manipulator  of  apparatus,  but  he  rarely 
is  required  to  trace  back  the  gradual  development  of 
the  subject  on  which  he  is  working.  It  remains  in  his 
mind  as  a  more  or  less  isolated  fragment,  since  he  is 
quite  ignorant  of  the  work  of  the  master  minds  of 
science  of  the  past.  When  he  leaves  the  school,  he  is 
impressed  by  the  head  of  his  department  with  the 
opinion  that  he  must  continue  his  research  work;  left 
to  his  own  devices  he  casts  about  for  new  problems, 
and,  in  despair  of  ideas,  continues  some  of  the  minor 
points  left  unsolved  in  his  thesis.  A  second  article 
appears  and  then  the  curtain  drops.  In  addition  to 
his  laboratory  work,  the  student  attends  lectures  in 
theoretical  science  and  passes  rigid  examinations  which 
are  for  the  most  part  exercises  in  ingenuity  in  mathe- 
matical and  logical  exposition  of  the  most  modern  and 
abstruse  parts  of  the  science.  The  lectures  treat  the 
science  as  a  modern  and  fully  developed  theory  devoid 
of  continuity  of  background.  Hypothesis  is  mixed 
with  fact,  and  fugitive  speculations  with  permanent 
laws;  his  texts  are  largely  confined  to  purely  specula- 


224        THE  LIMITATIONS  OF  SCIENCE 

tive  philosophy  and  fail  to  contrast  the  limitations  and 
the  permanent  achievements  of  science;  no  connection 
with  past  thought  is  drawn  and  the  probable  aspects 
of  future  thought  are  not  shown.  Indeed,  no  mention 
is  made  of  the  prime  fact  that  human  thought  has  been 
concerned  with  these  fundamental  problems  for  so 
many  centuries,  and  methods  of  scientific  attack  are 
so  limited  in  number,  that  no  new  theory  or  hypothesis 
can  be  developed;  witness  our  present  return  to  Car- 
tesianism.  At  most,  what  we  call  modern  thought  is 
but  a  recrudescence  of  past  thought  dressed  in  new 
clothing.  The  see-saw  of  the  time-worn  antinomies 
constantly  recurs.  Since  the  historical  and  critical 
attitude  toward  science  is  almost  wholly  neglected,  the 
student  enters  his  life  work  innocent  of  the  limitations 
and  powers  of  his  science;  practiced  in  modern  text- 
books and  ignorant  of  the  masters  of  the  subject. 
Some  teachers  of  science  realize  this  vaguely  and  ad- 
vise their  students  to  take  a  minor  in  philosophy.  Now 
the  philosophers,  not  knowing  science,  have  introduced 
certain  emasculated  courses  under  the  name  of  scien- 
tific philosophy  or  scientific  methods  for  just  such 
students.  One  has  merely  to  read  the  texts  used  and 
learn  the  views  of  the  expositors  to  find  that  the  texts 
are  written,  and  the  courses  delivered,  by  men  who 
know  nothing  of  science  at  first  hand.  Thus  the  course 
merely  discourages  the  student  and  gives  him  a  con- 
tempt for  philosophy  as  a  juggling  of  words  and  quite 


THE  ARBITER  OF  ETHICS  225 

different  from  the  exact  and  virile  sciences.  If  stu- 
dents of  science  are  ever  to  attain  to  the  wide  outlook 
which  the  dignity  of  science  deserves,  teachers  of  sci- 
ence must  themselves  first  learn  the  historical  and 
critical  development  of  their  subject,  establish  its  rela- 
tion to  other  knowledge,  and  then  impart  this  spirit  to 
their  neophytes. 

If  the  postulates  of  science  are  doubtful  and  con- 
tradictory, what  is  likely  to  be  the  effect  on  science 
and  thought  in  general  of  the  hypotheses  derived  from 
them?  The  very  general  belief  that  any  hypothesis, 
whether  false  or  not,  is  useful  to  science  puts  us  in 
a  curious  attitude  in  respect  to  other  methods  of 
thought.  Evidently,  it  is  a  doctrine  which  does  not 
hold  elsewhere;  the  theologian,  the  philosopher,  or  the 
historian  who  ventured  the  same  opinion  would  quickly 
be  attacked;  and  yet  science  is  supposed  to  be  the 
search  for  objective  truth.  The  reason  for  this  pecu- 
liar attitude  of  men  of  science  is  due  to  the  fact  that 
the  real  work  in  science  is  connected  with  phenomena 
and  laws,  and  this  true  aim  of  science  has  never  really 
been  lost  sight  of,  however  much  the  hypothetical 
method  may  have  distorted  it. 

I  suppose  it  may  be  granted  that  hypotheses  should 
be  divided  into  the  three  general  classes  of  the  good, 
the  false,  and  the  indifferent. 

Good  hypotheses  are  those  which  are  known  as  laws. 
They  are  generalizations  from  such  necessary  postu- 


226         THE  LIMITATIONS  OF  SCIENCE 

lates  as  the  conservation  of  matter  and  energy,  or  they 
are  advanced  as  tentative  laws  when  a  certain  number 
of  phenomena  can  conveniently  be  classified;  they  be- 
come steadily  more  exact  as  our  knowledge  of  the  sub- 
ject increases  and  are  finally  accepted  as  laws;  such 
has  been  the  history  of  the  second  law  of  thermo- 
dynamics, of  the  law  of  evolution,  and  numerous 
others.  The  difference  between  these  proper  hypoth- 
eses or  laws  and  other  hypotheses  is  that  a  law  does 
not  attempt  to  explain  the  mechanism  of  nature  as  an 
hypothesis  does.  That  is,  laws  may  be  readily  recog- 
nized because  they  deal  only  with  sensible  matter  and 
its  attributes  and  can  thus  be  subjected  to  a  rigid 
test  of  their  truth ;  all  other  hypotheses,  since  they  at- 
tempt to  explain  natural  actions,  must  create  fictitious 
substances  and  attributes  and  when  they  are  found  to 
depart  from  facts  they  are  not  discarded  but  are  merely 
modified  by  arbitrarily  altering  the  fictitious  substances 
on  which  they  depend.  This  difference  is  shown  clearly 
by  Darwin's  law  of  evolution  and  his  hypotheses  of 
natural  selection  and  pangenesis,  or  by  Newton's  law 
of  gravitation  and  his  hypothesis  of  light  corpuscles. 
The  history  of  science  points  to  no  more  certain  conclu- 
sion than  that  laws  persist  and  hypotheses  decay.  For 
this  reason,  I  have  emphasized  the  distinction  between 
the  two  and  have  limited  the  term,  hypothesis,  to  those 
scientific  theories  which  require  the  creation  of  fictitious 
substances  and  occult  forces  and  whose  use  has  caused 


THE  ARBITER  OF  ETHICS  227 

us  to  cross  those  boundaries  which  properly  limit  sci- 
ence. 

As  for  false  hypotheses,  it  would  seem  to  be  self- 
evident  that  they  should  be  abandoned  as  soon  as  a 
postulate  or  conclusion  was  shown  to  be  wrong.  It  is 
just  as  important  to  discard  error  in  science  as  it  is  in 
anything  else.  And  it  is  besides  an  added  and  con- 
fusing burden  to  the  student  to  keep  these  false  hypoth- 
eses in  treatises  on  science;  they  should  be  relegated  to 
histories  of  criticism  whose  chief  purpose  is  to  show  the 
progress  of  science  in  its  devious  path  toward  the 
truth. 

Unfortunately,  most  hypotheses  cannot  be  readily 
classed  as  either  true  or  false  since  they  involve  pos- 
tulates which  can  neither  be  denied  nor  affirmed  from 
scientific  criteria;  thus  in  themselves  they  are  fitly 
classed  as  indifferent.  Yet  they  may  indirectly  either 
benefit  or  obstruct  the  progress  of  science.  So  long 
as  we  keep  clearly  in  our  minds  and  in  our  statements 
the  fact  that  such  problems  as  a  nebular  hypothesis,  the 
condition  of  prehistoric  life,  radiation  in  interstellar 
space,  the  ultimate  constitution  of  matter,  etc.,  are 
pure  speculations,  I  do  not  suppose  any  serious  harm 
is  done.  But  the  hypotheses  which  we  have  created 
with  respect  to  atoms,  the  ether,  natural  selection, 
mutations,  and  the  like,  have  a  much  more  subtile  in- 
fluence, and  they  have  been  used  in  such  a  fashion  as 
to  confuse  knowledge. 


228        THE  LIMITATIONS  OF  SCIENCE 

Indifferent  hypotheses  will  have  a  pernicious  influ- 
ence if  by  their  use  the  deductions  of  science  become 
increasingly  complex.  Since  hypotheses  deal  with  con- 
fessedly fictitious  substances,  it  seems  rather  futile  to 
create  things  which  add  to  the  difficulty  of  a  problem. 

Again  we  find  our  hypotheses  are  becoming  so  ab- 
struse that  they  require  a  prolonged  technical  training 
and  specialization  before  they  can  be  understood ;  thus 
the  science  itself  is  restricted  to  a  few  specialists  and 
loses  much  power.  These  abstruse  hypotheses  are 
producing  a  breach  even  between  theoretical  and  ex- 
perimental science.  So  marked  is  the  difference  be- 
tween these  two  aspects  of  the  same  science  that  they 
have  little  in  common  and  are  frequently  hostile. 

But  the  most  inevitable  and  dangerous  influence  of 
the  free  use  of  indifferent  hypotheses  is  the  breaking 
down  of  the  scientific  method  by  carrying  science  into 
fields  where  it  has  no  business  to  be.  I  have  tried  to 
show  what  the  limitations  of  science  are  and  why  the 
obliteration  of  its  boundaries  is  prejudicial  to  it.  In 
what  has  gone  before,  the  discussion  has  been  limited 
to  excursions  into  what  may  be  called  pseudo-science. 
Encouraged  by  lack  of  criticism,  there  is  now  a  desire 
to  go  much  further  and  to  claim  that  science  is  the 
sovereign  of  all  knowledge.  Thus,  the  example  given 
in  the  last  chapter  of  Sir  Oliver  Lodge's  attempt  to 
include  the  phenomena  of  immortality  in  the  field  of 
science  is  undoubtedly  made  possible  by  the  steady  ^ 


THE  ARBITER  OF  ETHICS  229 

and  gradual  trend  toward  treating  matter  symbolically. 
The  step  between  considering  matter  as  tangible  reality 
and  as  Poincare's  hole  in  the  ether  is  really  greater 
than  passing  from  material  to  immaterial  phenomena 
or  than  maintaining  that  science  is  the  guide  of  char- 
acter and  the  arbiter  of  ethics.  In  this  way  scientific 
naturalism  is  more  dangerous  than  the  easily  refuted 
outbreak  of  Sir  Oliver  Lodge. 

Any  system  of  ethics  must  aim  to  develop  character; 
it  must  establish  a  standard  of  good  and  evil;  it  must 
judge  actions  according  to  this  standard  and  provide 
an  inner  check  which  will  restrain  the  will  of  the  indi- 
vidual. But  scientific  experimentation  and  theory  do 
not  directly  consider  character  at  all.  The  attempt  is 
there  made  to  discover  objective  facts  and  laws  which 
have  no  character  in  themselves  and  to  manipulate 
or  interfere  with  natural  forces  so  that  they  will 
add  to  our  knowledge  and  power.  No  one  would 
hesitate  to  say  that  the  discovery  of  the  laws  of 
heat  and  their  application  to  steam  power  were  prob- 
lems definitely  in  the  field  of  scientific  investigation  or 
that  they  had  added  enormously  to  our  power. 
They  have  in  fact  changed  civilization,  and  yet 
we  cannot  deduce  from  science  whether  or  not 
this  acquisition  of  power  has  been  accompanied 
by  a  beneficial  effect  on  civilization.  That  can 
be  determined  only  by  the  moral  effect  of  the 
expansion  of  industrialism  on  the  inner  life  and 


230        THE  LIMITATIONS  OF  SCIENCE 

thoughts  of  men,  and  science  has  no  criteria  for  these. 
The  man  of  science  is  thus  trained  to  discover  new 
things.  He  may  point  out  their  dangers  and  advantages 
but  the  restrictions  to  be  placed  upon  their  use  is  not 
his  affair. 

If  we  were  to  trace  the  growth  of  the  idea  that  the 
scientific  method  is  our  best  means  of  obtaining  in- 
formation not  only  of  objective  facts  but  also  of  the 
motives  of  human  thought  and  character,  it  would  re- 
quire a  detailed  history  of  science.  But  without  under- 
taking so  laborious  a  task,  certain  prominent  factors 
in  the  rise  of  science  can  be  indicated.  In  the  first 
place  we  may  assert  that  the  guide  of  science  during 
the  early  and  medieval  periods  was  the  Organon  of 
Aristotle.  And  we  can  also  state  pretty  accurately 
that  the  revolution  in  science  against  the  Aristotelian 
domination  was  accomplished  under  the  leadership  of 
Albert  of  Saxony,  Leonardo  da  Vinci,  Copernicus, 
Galileo,  and  Descartes. 

The  aim  of  these  revolutionists  was  to  replace  the 
metaphysical  method  of  Aristotle  by  the  physical  or 
experimental  method.  To  put  the  issue  simply,  the 
purpose  of  the  Aristotelian  philosophers  was  to  form 
a  comprehensive  and  logical  system  of  the  universe 
as  they  conceived  it  should  be,  a  philosophy  in  which 
experimental  observation  and  inductive  reasoning 
played  but  a  minor  role;  the  scientific  method  of  the 
new  school  aimed  to  determine  the  laws  of  a  universe 


THE  ARBITER  OF  ETHICS  231 

which  would  be  in  accord  with  the  phenomena  dis- 
covered by  experiment.  Naturally  the  division  was  not 
sharp;  even  to  Galileo,  and  especially  to  Descartes, 
much  of  the  Aristotelian  method  still  clung. 

Just  as  the  Or g anon  of  Aristotle  absorbed  the  sci- 
entific spirit  of  the  Greeks,  so  we  have  in  the  Novum 
Organum  of  Bacon  an  explicit  attempt  to  crystallize 
the  new  knowledge  into  a  scientific  method.  To  make 
his  purpose  quite  clear  he  invented  for  it  a  new  name, 
natural  philosophy,  so  as  to  separate  it  from  the  meta- 
physical philosophy  of  the  Greeks.  This  natural 
philosophy,  if  carried  out  logically,  would  limit  us  to 
the  laborious  and  careful  accumulation  of  experimental 
facts,  out  of  which  would  grow  true  natural  laws. 
And,  further  to  show  the  break  he  would  make  with 
the  Peripatetic  school,  he  states  that  any  further  gen- 
eralization which  would  lead  to  the  consideration  of 
formal  and  final  causes  must  require  a  hypothetical 
method  proper  only  to  metaphysics.  His  criticism 
of  Greek  philosophy  is  characteristic  of  his  attitude. 
Thus  he  gives  his  well-known  opinion  that  the  Greeks 
were  a  vain  and  disputatious  people,  whose  desire  to 
shine,  whose  taste  for  dispute,  and  whose  mania  for 
new  systems  of  thought  multiplied  error,  leading  them 
to  forsake  observation  for  the  more  facile  triumphs 
of  speculation.  Nor  did  he  spare  the  greatest,  when 
he  declared  that  Plato  subordinated  the  world  to  ideas ; 
and  Aristotle,  ideas  to  words.  The  one  corrupted  sci- 


232        THE  LIMITATIONS  OF  SCIENCE 

ence  by  theology  and  the  other  by  dialectics,  as  later 
Proclus  did  by  mathematics.  And  while  we  have 
learned  by  experience  that  scientific  laws  are  not  to  be 
discovered  by  such  a  regulated  system  of  induction 
because  science  does  not  rest  on  a  single  broad  founda- 
tion which  rises  uniformly,  like  an  Egyptian  pyramid, 
to  a  point  that  signifies  a  single  dominant  force,  yet 
Bacon's  inductive  philosophy  is  still  our  authoritative 
scientific  method.  In  this  opinion  we  have  the  un- 
qualified statements  of  such  men  as  Newton,  Huygens, 
and  Laplace.  Thus  Laplace  expresses  most  clearly 
what  men  of  science  even  now  generally  admit :  "  La 
methode  la  plus  sure  qui  puisse  nous  guider  dans  la 
recherche  de  la  verite  consiste  a  s'elever  par  induction 
des  phenomenes  aux  lois  et  des  lois  aux  forces.  Les 
lois  sont  les  rapports  qui  lient  entre  eux  les  phenomenes 
particuliers :  quand  elles  ont  fait  connaitre  le  principe 
general  des  forces  dont  elles  derivent,  on  le  verifie  soit 
par  des  experiences  directes,  lorsque  cela  est  possible, 
soit  en  examinant  s'il  satisfait  aux  phenomenes  connus; 
et  si  par  une  rigoureuse  analyse,  on  les  voit  tous 
decouler  de  ce  principe,  j  usque  dans  leur  moindres 
details,  si  d'ailleurs  ils  sont  tres-varies  et  tres-nom- 
breux,  la  science  alors  acquiert  le  plus  haut  degre  de 
certitude  et  de  perfection  qu'elle  puisse  atteindre. 
Telle  est  devenue  I'astronomie  par  la  decouverte  de  la 
pesanteur  universelle." 

It  is  natural  that,  if  observation  is  the  only  sure 


THE  ARBITER  OF  ETHICS  233 

guide  to  natural  philosophy  and  if  knowledge  must 
finally  rest  on  the  sensations,  Bacon  would  be  consid- 
ered by  many  as  the  founder  of  the  doctrine  elaborated 
by  Locke,  Hobbes,  Hume,  and  others  that  there  is  noth- 
ing in  the  intelligence  which  has  not  previously  been  a 
matter  of  the  sensations.  But  as  de  Remusat  *  points 
out :  "  To  say  that  in  life  all  knowledge  is  derived 
only  from  the  data  of  experience,  and  to  say  that 
everything  which  is  in  the  intellect  has  been  a  matter 
of  the  senses,  is  to  say  two  immensely  different  things. 
And  Bacon  has  not  said  the  second  of  these  two  things ; 
he  has  not  even  said  absolutely  the  first;  he  admits  in- 
spired knowledge."  That  is,  Bacon  apparently  divided 
knowledge  into  classes,  the  physical  and  the  metaphysi- 
cal, and  based  the  former  only  on  the  sensations.  In 
confirmation  of  this  opinion  Bacon  took  a  positive  stand 
against  atheism :  "  No  one  denies  the  existence  of  the 
gods,  except  him  to  whom  it  is  serviceable  that  the 
gods  do  not  exist.  To  deny  God,  is  to  destroy  the 
nobility  of  the  human  race." 

There  seems  then  good  reason  for  considering  the 
Novum  Orgqmim  as  the  starting-point  of  modern  sci- 
ence, as  in  it  is  developed  the  doctrine  which  still  pre- 
vails, that  science  must  depend  on  observation,  and 
that  scientific  theory  must  conform  to  the  data  of 
experience. 

*  Vie  de  Bacon,  p.  266. 


234        THE  LIMITATIONS  OF  SCIENCE 

While  it  is  true  that  Bacon  maintained  a  distinction 
between  those  things  which  are  proper  for  scientific 
elucidation  and  those  things  which  are  not;  and  al- 
though he  avoided  a  universal  philosophy  of  the  sensa- 
tions; yet  his  predilection  for  the  scientific  method  and 
his  inclusion  in  it  of  such  subjects  as  history,  which 
in  spite  of  time  and  effort  has  made  little  progress  as 
a  science,  pointed  the  road  to  that  philosophy.  So  also 
some  believe  him  to  be  the  originator  of  the  idea  of 
applying  the  scientific  method  to  society  and  ethics. 
Such  does  not  seem  to  be  correct  and  I  think  it  is  not 
possible,  because  the  rule  of  science  over  life  could  not 
have  been  accomplished  until  a  great  accumulation  of 
scientific  observations  had  been  made.  No  such  ac- 
cumulation had  been  undertaken  before  the  last  cen- 
tury. In  Bacon's  time  only  a  few  enlightened  minds 
were  convinced  of  the  need  of  systematic  experimental 
knowledge.  Even  the  British  school  of  philosophers, 
known  as  rationalists,  materialists,  or  atheists,  who 
were  more  or  less  followers  or  supposed  to  be  followers 
of  Bacon,  was  a  school  of  metaphysicians  and  not  of 
scientists. 

Of  these  philosophers,  Hpbbes  undoubtedly  had  more 
of  the  scientific  closeness  of  reasoning  than  the  others. 
He  based  all  knowledge  on  the  sensations  and  in  so 
far  seems  to  exalt  science  to  be  the  arbiter  of  life,  but 
nothing  could  be  less  scientific  than  the  postulates  and 
the  conclusions  of  his  philosophy.  He  had  little  reali- 


THE  ARBITER  OF  ETHICS  235 

zation  of,  and  much  contempt  for,  experimental  knowl- 
edge. He  assumed  certain  abstract  definitions  as  uni- 
versal postulates  and  from  them  derived  all  his  con- 
clusions by  pure  ratiocination  without  any  regard  as 
to  whether  these  conclusions  conformed  to  objective 
facts.  A  brief  glance  at  some  of  the  definitions  and 
deductions,  which  may  be  found  in  his  Leviathan,  will 
show  that  he  was  advancing  a  purely  metaphysical  sys- 
tem of  thought.  Thus,  every  part  of  the  universe  is 
body.  Bodies  comprise  those  things  which  are  formed 
by  nature  and  commonly  called  bodies  and  those  formed 
by  the  human  will  which  we  call  societies;  this  latter 
idea  still  lingers  in  the  phrase,  the  body  politic.  Mo- 
tion is  the  cause  of  all  things,  even  of  the  human  pas- 
sions, etc.  The  small  beginnings  of  motion  within  the 
body  of  man  before  they  appear  in  walking,  speaking, 
striking,  and  other  visible  actions,  are  commonly  called 
endeavor.  Endeavor,  when  it  is  toward  some  thing 
which  causes  it,  is  called  appetite,  or  desire.  He  dis- 
tinguishes in  the  following  and  entirely  arbitrary 
fashion  between  the  sensations.  Heat  is  motion  re- 
sulting from  the  light  endeavor;  hearing  is  generated 
by  the  motion  of  the  medium,  but  not  in  the  same  man- 
ner as  seeing.  Sight  is  an  endeavor  from  pressure 
produced  by  the  luminous  body  on  the  retina  of  the  eye, 
and  by  the  pressure  on  that  part  it  will  be  propagated 
to  the  heart,  the  innermost  organ  of  sight  and  of  all 
the  senses;  and  from  the  reaction  of  the  heart,  in  which 


236        THE  LIMITATIONS  OF  SCIENCE 

reaction  consisteth  the  nature  of  sense,  there  will  pro- 
ceed an  endeavor  back  to  the  retina.  This  endeavor 
outwards  is  the  thing  called  light,  or  the  phantasm  of  a 
lucid  body.  From  this  utter  confusion  of  bodies, 
subjective  and  objective,  physical  and  political,  and 
motions,  real  and  occult,  proceed  his  deductions.  It  is 
no  wonder  that  he  had  continual  controversies  about 
scientific  questions,  in  which  he  was  always  worsted. 
One  of  the  most  famous  resulted  from  his  explanation 
of  the  barometer.  In  his  desire  to  assume  body  for 
everything  he  was  forced,  as  was  Descartes,  to  include 
space  in  the  category  of  substance.  So  to  account  for 
the  space  above  the  mercury,  he  asserted  that  air  passed 
in  and  out  through  the  mercury  because  he  had  pre- 
viously stated  that  a  vacuum  was  a  body  which  could 
not  be  increased  or  diminished.  Enough  has  been 
given  to  show  that  Hobbes  was  not  a  man  of  science 
and  that  his  method  was  not  the  scientific  method; 
and  the  same  can  be  shown  with  certainty  of  all 
philosophers  who  flourished  previously  to  the  nineteenth 
century.  It  was  not  until  then  that  a  systematic  and 
large  accumulation  of  scientific  observations  of  all 
sorts  was  at  hand.  Even  now,  the  biological  sciences 
are  the  only  ones  possible  as  a  guide  to  ethics  because 
the  mathematical  sciences,  physics,  astronomy,  and 
chemistry,  are  too  remote  from  human  passions  and 
emotions  to  be  serviceable. 

Apparently  in  the  biological  sciences  it  was  neces- 


THE  ARBITER  OF  ETHICS  237 

sary  to  wait  for  the  promulgation  of  the  law  of  evolu- 
tion before  a  nexus  could  be  formed  between  the  ma- 
terial and  spiritual  aspects  of  nature.  For  it  seems 
clear  that  such  a  system  of  ethics  must  substitute  the 
worship  of  nature  for  the  worship  of  God  if  science 
is  to  become  the  guide  to  conduct.  That  is,  some  prin- 
ciple of  nature,  subject  only  to  physical  laws,  must 
work  toward  perfection  in  man  in  the  ordinary  sense 
of  guiding  his  aspirations  toward  absolute  goodness, 
and  thus  supply  a  check  and  interference  to  his  actions ; 
a  check  which  metaphysical  systems  have  always  ac- 
complished by  assuming  an  outside  and  supernatural 
force,  which  is  not  restricted  by  natural  law. 

On  first  sight,  the  biological  sciences,  with  evolu- 
tion as  a  guiding  principle,  offer  a  promising  field  for 
a  system  of  ethics  which  shall  depend  on  natural  law 
and  be  positive  in  that  it  does  not  introduce  the  occult 
and  supernatural.  It  seemed  necessary,  during  the 
Victorian  age,  only  to  have  implicit  confidence  in  evo- 
lution and  to  let  the  machine  work  out  its  own  destiny, 
confident  that  all  was  well.  Thus  we  have  doctrines 
of  humanitarianism  and  evolution  in  the  poetry  of 
Tennyson  who  trusts  to  that  "  one  far-off  divine  event, 
to  which  the  whole  creation  moves."  We  have  the  same 
confidence  shown  by  Wordsworth  who  sucks  his  moral- 
ity from  flowers  and  stones,  or  by  Fiske  who  writes  his 
moral  confession  in  an  essay  entitled  w  Through  Na- 
ture to  God."  But  all  is  not  so  simple  or  even  so 


238        THE  LIMITATIONS  OF  SCIENCE 

scientific  as  Spencerian  philosophy  would  have  us  be- 
lieve. 

The  doctrine  of  evolution,  as  a  strictly  scientific  law, 
states  merely  that  the  different  species  of  animals  and 
plants  were  not  created  as  distinct  types  but  that  they 
have  gradually  changed  by  a  progressive  modification 
until  each  existing  species  is  the  last  surviving  branch 
or  twig  of  the  biological  tree.  Evidently,  then,  all  life 
can  be  traced  back,  if  we  could  gather  up  the  tangled 
and  broken  skein  of  life,  either  to  one  or  at  least  to  a 
few  prototypes.  Now  the  law  of  evolution  takes  no 
account  of  good  or  bad,  of  high  or  low,  or  of  the 
method  by  which  one  species  has  changed  to  another. 
According  to  it,  each  type  has  maintained  its  continued 
existence  simply  because  certain  of  its  attributes  have 
given  it  an  advantage  over  its  competitors.  From 
observation  we  find  that  those  types,  we  think  to  be 
primitive,  are  simpler  in  construction  and  functions 
than  are  those  we  suppose  to  be  later.  But  it  is  by 
no  means  a  universal  law  that  simple  types  change 
to  complex  ones,  witness  the  persistence  of  microbes 
and  bacilli.  The  law  of  evolution  is  thus  a  scientific 
law  which  attempts  to  generalize  a  set  of  phenomena 
observed  objectively  and  has  nothing  to  do  with  ethics 
or  what  I  have  called  character. 

What  may  be  called  the  ethical  aspect  of  evolution 
has  been  injected  into  it  by  hypothetical  or  metaphysical 
reasoning.  Darwin  and  his  successors,  generally,  have 


THE  ARBITER  OF  ETHICS  239 

attempted  also  to  find  the  causes  of  evolution  and  the 
mechanism  of  heredity.  And  here  all  is  confusion, 
and,  as  occurred  in  the  physical  sciences,  each  theorist 
sets  up  his  own  scheme  of  natural  selection,  of  pan- 
genesis,  of  mutation  and  what  not,  and  the  battle 
without  an  issue  rages  fiercely.  In  the  first  place,  a 
purely  anthropomorphic  aspect  is  given  to  evolution  by 
the  unjustifiable  use  of  the  terms  higher  and  lower 
forms  of  life.  These  words  can  signify  merely  the 
comparison  between  two  types  as  regards  their  com- 
plexity of  functions.  It  is  only  by  regarding  man  as 
the  goal  toward  which  all  creation  tends,  that  we  can 
call  those  types  the  highest  which  most  nearly  resemble 
man.  The  final  step  is  easy  and  the  word  "  high  "  in 
evolution  is  transferred  to  the  derived  sense  of  mean- 
ing noble  and  good.  It  would  be  a  most  interesting  and 
useful  work  to  trace  back  this  curious  and  persistent 
habit  of  linking  high  and  low  as  space  attributes,  to 
high  and  low  as  ethical  concepts.  Much  of  our  con- 
fusion of  thought  comes  from  such  loose  use  of  words, 
and  few  of  us  can  quite  rid  our  minds  of  the  impression 
that  hell  and  evil  are  beneath  us,  and  heaven  and  joy 
above  us.  At  all  events,  the  metaphorical  use  of  these 
words  seems  to  have  done  much  to  change  the  imper- 
sonal law  of  evolution  into  a  sort  of  deity  which  de- 
velops the  lowly  algae  into  a  choir  of  angels. 

If  we  attempt  to  discover,  in  a  general  way,  the 
cause  of  evolution,  we  must  ascribe  it  either  to  a  super- 


24o        THE  LIMITATIONS  OF  SCIENCE 

natural  or  to  a  natural  force.  The  variation  of  species 
may  be  due  to  a  supernatural  power  which  created  a 
protoplasm  and  then  guided  organic  life  through  the 
slow  developing  ages.  But  to  us  such  a  form  of 
creation  is  as  little  scientific  as  the  cosmogony  of  the 
Book  of  Genesis.  Scientific  hypotheses  must  avoid  the 
supernatural  and,  however  they  differ  in  details,  they 
must  base  evolution  on  the  natural  laws  of  probability 
and  chance,  using  these  words  in  their  technical  sense 
of  expressing  the  statistical  actions  of  physical,  chem- 
ical, or  biological  forces  on  molecular  masses.  In 
natural  or  scientific  law  there  can  be  assumed  no  escape 
from  the  calculable  action  of  a  force.  Given  effects  fol- 
low from  given  causes  and  these  must  precede  each 
other  with  uniform  regularity,  back  as  far  as  we  care 
to  carry  the  law.  In  this  manner  we  have  formulated 
a  law  of  evolution  without  introducing  the  idea  of 
ethics  at  all.  And  so  far  as  the  question  concerns 
ethics  it  is  restricted  to  a  minute  province,  man,  in  the 
vast  empire  of  life.  Thus  we  have  made  an  absolute 
break  in  the  law  of  evolution;  on  one  side  is  the  un- 
moral development  of  all  the  universe,  and  on  the  other 
side  is  the  moral  growth  of  man.  At  least  in  our 
egotism  we  reserve  the  attribute  of  character,  or  of 
judging  actions  as  good  or  evil,  to  ourselves.  It  is 
almost  useless  to  add  that  a  law  of  continuous  develop- 
ment, like  evolution,  with  such  a  break  in  it  is  far  from 
perfect. 


THE  ARBITER  OF  ETHICS  241 

We  shall  therefore  confine  ourselves  to  the  law  of 
evolution  only  so  far  as  it  relates  to  man.  And  let  us 
in  the  first  place  reject  rigorously  the  sentimental 
opinions  of  a  class  of  writers  who  twist  the  laws  of 
nature  into  a  kind  of  beneficial  providence.  The  inex- 
orable forces  of  nature  teach  us  the  survival  of  the 
strong  and  the  elimination  of  the  weak;  the  fatal 
progress  of  the  inanimate  universe  riding  over  and 
crushing  whatever  disobeys  its  laws,  without  hate  but 
without  ruth,  is  not  calculated  to  inspire  an  enlightened 
and  exclusive  student  of  science  to  regard  with  con- 
sideration this  personification  of  nature  as  a  type  of 
human  love  which  would  cherish  the  sick  and  teach 
self-abnegation  to  the  strong. 

Nor  can  we  discover,  during  historic  times,  much 
change  in  the  physique  or  in  the  character  of  men.  And 
we  are  forced  to  agree  with  Huxley,  who  believed  that 
the  laws  of  natural  evolution  ceased  to  be  operative  on 
man  when  self -consciousness  became  developed  in  him. 
In  the  prolegomena  to  Evolution  and  Ethics  he  intro- 
duces a  vivid  picture  in  which  he  portrays  natural 
evolution  of  animals  and  plants  as  life  in  a  forest.  The 
characteristic  feature  of  this  life  is  an  intense  and 
unceasing  competition  in  the  struggle  for  existence. 
In  the  untamed  forest,  the  cosmic  forces  use  unre- 
stricted multiplication  as  their  principal  aid ;  for  every 
violet  or  for  every  oak  that  grows,  thousands  die, 
crushed  without  a  compunction.  There  must  be 


242         THE  LIMITATIONS  OF  SCIENCE 

strength  and  flexibility  and  good  luck  that  plants  and 
animals  may  attain  congenial  places  and  invade  suc- 
cessfully large  areas.  On  the  other  hand,  the  habita- 
tion of  man  may  be  considered  as  life  in  a  cultivated 
garden,  where  the  gardener  restricts  multiplication, 
gives  each  plant  space  and  nourishment,  and  shields  it 
from  the  vicissitudes  of  climate.  He  uproots  the  nat- 
ural inhabitants,  modifies  the  soil  and  conditions  to 
suit  exotics,  and  gives  the  weak  equal  advantages  with 
the  strong.  As  a  result,  natural  evolution  has  become 
so  modified  and  weakened  that  man  is  in  a  class  by 
himself,  and  develops  under  different  laws  from  the 
rest  of  the  world. 

So  far  as  I  can  see,  nothing  in  biology  has  been  dis- 
covered which  contradicts  this  opinion  of  Huxley.  It 
is,  however,  difficult  to  see  how  and  when  a  break  of 
so  fundamental  a  nature  between  man  and  the  rest 
of  life  could  occur  in  a  continuous  evolution  in  which 
man  is  included.  But  it  seems  certain  that  man  has 
attained  to  so  complex  and  rich  a  character,  his  aims 
are  so  diversified,  that  any  law  of  evolution  of  his 
future  development  simple  enough  for  us  to  compre- 
hend is  out  of  the  question.  Where  any  such  a  law 
would  operate  to  emphasize  a  certain  attribute,  it  would 
diminish  another  which  would  be  considered  by  many 
to  be  equally  important.  Instead  of  strength,  flexi- 
bility, and  good-luck  only,  there  are  a  thousand  other 
influences  to  be  balanced. 


THE  ARBITER  OF  ETHICS  243 

If  we  are  to  found  ethics  on  biology  and  evolu- 
tion we  are  driven  to  inventing  a  sort  of  spiritual  evo- 
lution which  is  best  expressed  by  the  term  naturalism. 
And  if  anyone  will  consider  the  systems  of  this  kind 
which  are  proposed  as  guides  to  society,  I  think  he  will 
find  that  they  may  all  be  included  in  this  one  general 
type.  There  seem  to  be  four  possible  ways  of  account- 
ing for  an  evolution  of  the  race.  Humanity  may  be 
guided  to  a  goal  of  perfection  by  some  divine  and 
omniscient  external  power  which  imposed  certain  initial 
laws  of  nature  and  permits  a  subsequent  evolution  to 
progress  without  interference;  humanity  may  contain 
in  itself  such  a  directing  force;  it  may  be  constrained 
toward  a  future  condition  by  the  conscious  effort  of 
a  set  of  judges  who  will  determine  and  enforce  the 
manner  of  its  evolution;  lastly,  society  may  divide 
into  two  classes,  those  who  by  superior  knowledge  and 
power  fulfill  their  destiny  at  the  expense  of  the  op- 
posite class  of  the  ignorant  and  weak. 

If  we  bear  in  mind  that  science  is  not  only  the  study 
of  natural  law  as  an  objective  series  of  events,  but 
that,  if  it  is  to  have  any  application  to  the  needs  and 
desires  of  society,  the  natural  balance  and  operation 
of  forces  and  energy  must  be  interfered  with,  then  it 
is  easy  to  see  that  the  first  two  doctrines  of  naturalism 
are  not  scientific.  To  say  that  the  human  race  is 
guided  to  a  goal  of  perfection,  previously  determined, 
by  either  an  external  and  divine  power  or  by  some 


244        THE  LIMITATIONS  OF  SCIENCE 

omniscient  power  existing  in  society  itself,  is  to  deny 
and  abstract  from  the  individual  the  basic  axiom  of 
science  that  the  laws  of  nature  may  be  interfered 
with. 

The  third  class,  which  leaves  the  guidance  of  the 
evolution  of  the  race  more  or  less  under  the  control 
of  individuals  composing  it,  is  properly  a  scientific 
method,  because  it  postulates  an  objective  world  sub- 
ject to  laws  and  permits  of  their  modification.  This 
type  of  naturalism  has  already,  under  the  name  of 
eugenics,  attained  a  very  considerable  vogue,  and  it 
is  heralded  as  the  long  sought  guide  to  righteousness. 
It  is  worth  while  to  consider  its  claims  both  as  a 
science  and  as  a  system  of  ethics. 

Since  the  science  of  physics  has  developed  the  sci- 
entific method  more  consciously  and  more  accurately 
than  any  other  of  the  sciences,  we  may  turn  to  it  for 
an  illustration  of  the  method  to  be  followed  by  eugen- 
ists.  In  the  first  place,  the  experimenter  puts  himself 
in  the  position  of  being  external  to  the  phenomena  he 
expects  to  investigate.  He  also  decides  beforehand 
on  the  object  of  the  experiment;  that  is,  he  has  some 
definite  idea  which  he  wishes  to  confirm  or  contra- 
dict. He  then  observes  and  tabulates  the  phenomena 
which  are  relative  to  the  problem  and  abstracts  from 
them  all  the  actions  which  complicate  the  result  and 
are  not  essential  to  it.  But  as  he  invariably  finds  that 
the  free  and  unconstrained  phenomena  are  too  com- 


THE  ARBITER  OF  ETHICS  245 

plex  to  be  manageable  he  must  interfere  with  natural 
actions  and  rearrange  them.  Lastly,  his  observations 
are  to  be  classified  by  a  logical  process  into  laws. 

To  apply  this  scientific  method  to  the  development 
of  an  ethical  system  which  shall  conform  to  the  con- 
clusions of  biology,  certain  individuals  or  a  class  of 
individuals  must  act  as  experimenters,  distinguish 
themselves  from  the  rest  of  society,  and  regard  its 
actions  as  objective  phenomena  which  do  not  apply, 
for  the  time  being,  to  themselves.  These  experimental- 
ists must  acquaint  themselves  with  the  object  of  their 
experiment  and  interfere  with  the  unconstrained  ac- 
tions of  society  by  providing  constraints  which  shall 
control  and  direct  its  complex  course  into  simpler  chan- 
nels; and  finally  they  must  coordinate  the  effects  of 
these  constraints. 

Such  should  be  the  aim  of  what  is  popularly  known 
as  the  science  of  eugenics.  By  derivation,  eugenics 
means  to  be  born  well,  and  since  the  results  of  good 
birth  may  be  counteracted  by  the  subsequent  life  of  the 
individual,  a  second  science  has  been  added  currently 
under  the  title,  euthenics,  which  may  be  defined  as  the 
science  of  living  well.  For  the  sake  of  simplicity  let  us 
use  the  word,  eugenics,  to  include  this  entire  system  of 
scientific  ethics.  And  let  us  put  out  of  our  minds  im- 
mediately the  idea  that  the  eugenists  are  concerned 
with  the  simpler  problem  of  the  well-being  of  the  in- 
dividual; like  all  avowed  men  of  science,  they  attempt 


246         THE  LIMITATIONS  OF  SCIENCE 

to  deal  with  classes  of  phenomena.  In  this  instance, 
the  object  is  to  mold  the  whole  human  race,  with  its 
immensely  complex  and  diversified  desires  and  actions, 
its  egotisms  and  its  sympathies,  into  a  homogeneous 
society  which  shall  progress  toward  a  standard,  previ- 
ously determined,  of  a  noble  and  god-like  humanity. 
The  reward  to  be  expected  by  the  individual  who  is 
born  and  lives  well  is  that  intense  feeling  of  satisfac- 
tion he  will  have  that  the  race  as  a  whole  has  been 
carried  a  little  closer  to  a  distant  and  vague  goal  of 
perfection  because  of  his  submission  to  the  laws  of 
eugenical  righteousness. 

We  can  now  define  the  eugenists,  if  our  ideas  be  cor- 
rect, as  a  band  of  human  beings  who  shall  be  the  ar- 
biters of  right  and  wrong.  This  band  must  be  small 
because  it  is  difficult  to  find  even  two  persons  who  have 
the  same  standards;  it  must  be  select  as  there  is  at 
present  no  known  way  for  a  person  to  exercise  a  choice 
in  his  parents  and  it  will  need  judges  of  superior 
ability  to  pick  out  those  who  are  worthy  to  be  parents 
and  to  live.  Parentage  under  eugenical  guidance  is 
certain  to  be  a  very  serious  matter  and  I  imagine  that 
we  should  expect  a  rather  large  diminution  in  the 
human  race  for  a  few  centuries  until  the  system  is 
running  smoothly.  At  present,  we  cannot  leave  the 
regulation  of  life  after  birth  according  to  euthenic 
standards  to  the  ordinary  person,  because  we  should 
then  not  have  euthenics  at  all,  but  the  present  hap- 


THE  ARBITER  OF  ETHICS  247 

hazard  society.  So  we  must  take  it  for  certain  that  all 
people  must  be  born  and  live  according  to  the  regula- 
tions of  a  band  of  superior  human  beings. 

Having  thus  settled  on  the  organizers  of  experiments 
for  this  science,  their  next  step  will  be  to  arrange 
the  experiments  and  to  carry  them  out.  They  will 
first,  in  order  to  work  intelligently,  decide  what  are  the 
qualities  of  human  perfection.  I  cannot  discover  that 
this  has  been  done.  There  seems  to  be  just  as  great 
diversity  of  opinion  as  to  what  constitutes  the  perfect 
man  among  the  eugenists  as  there  is  among  ordinary 
men.  We  meet  so-called  eugenic  babies  and  euthenic 
adults,  but  as  standards  they  are  rather  disappointing 
and  do  not  seem  to  be  sufficiently  differentiated  from 
other  people.  Perhaps  this  is  to  be  expected,  for  true 
eugenics  is  a  slow  process.  With  the  goal  established, 
the  experimenters  must  then  find  some  scientific  way 
of  propagating  the  race  eugenically  and  of  determin- 
ing and  applying  constraints  or  checks  on  our  free 
manner  of  life  which  will  make  all  individuals  live 
euthenically. 

If  such  a  scientific  method  were  practicable,  it  would 
seem  to  a  physicist  that  a  system  of  ethics  could  be 
established  by  it.  But  it  is  a  question  whether  such  a 
system,  minimizing  as  it  must  the  check  of  personal 
responsibility,  would  not  fail  because  it  would  result  in 
a  form  of  intellectual  slavery.  So  far  the  doctrines  of 
modern  eugenics  have  not  shown  the  slightest  indica- 


248         THE  LIMITATIONS  OF  SCIENCE 

tion  of  scientific  method;  they  are  vague  and  char- 
•  acterized  by  a  lack  of  any  accurate  thinking.  Indeed, 
it  is  difficult  to  obtain  an  idea  of  what  the  eugenists 
aim  to  do  or  how  they  expect  to  work.  Curiously 
enough,  considering  his  lack  of  scientific  training,  Plato 
seems  to  be  the  one  who  saw  the  problem  clearly  and 
attempted  a  real  solution.  His  belief,  that  every  per- 
son desired  to  be  born  well  and  to  live  well  if  only 
he  knew  how,  appeals  to  one  as  an  explicit  statement 
of  eugenics.  That  is,  if  we  could  eliminate  ignorance 
and  regulate  our  passions,  society  would  advance  to 
an  ideal  state,  and  in  his  Republic,  Plato  sketches 
such  a  polity  in  detail.  The  failure,  for  failure  it  was, 
came  from  his  inability  to  define  what  ignorance  is  or 
how  to  check  our  passions.  His  ideal  state  is  not  only 
impracticable,  but  if  adopted  would  result  in  political 
slavery. 

If  we  examine  somewhat  in  detail  what  is  being  done 
to  make  a  science  of  eugenics  and  to  apply  it  to  regu- 
late the  affairs  of  men,  we  shall  find  that  it  is  in  no 
sense  a  science  and  is  singularly  unfit  to  accomplish 
such  a  purpose. 

In  the  first  place  there  are  no  judges  who  are  ac- 
cepted, or  likely  to  be  accepted,  as  having  any  unanimity 
of  purpose  or  plan.  Ethical  systems,  in  the  past,  have 
been  born  in  the  heart  and  mind  of  a  single  man,  who 
was  recognized  as  one  endowed  with  a  peculiar  power 
of  righteousness  and  whose  life  had  become  an  ex- 


THE  ARBITER  OF  ETHICS  249 

ample.  So  necessary  was  it  to  have  an  example  of  per- 
fection which  should  not  be  subject  to  the  waywardness 
of  human  passions,  that  without  exception  all  religions 
assign  divine  attributes  to  their  founders.  And  in 
order  to  maintain  the  integrity  and  the  unanimity  of 
belief  in  even  a  sect,  the  rest  of  society,  with  its  con- 
flicting purposes,  has  always  been  explicitly  banished 
from  communion  with  the  faithful. 

The  case  of  eugenics  is  quite  different.  To  be  a  sci- 
ence it  must  deal  with  the  race  and  not  with  indi- 
viduals; instead  of  a  founder,  to  whom  are  ascribed 
divine  or  at  least  superhuman  powers  and  who  makes 
an  appeal  to  sympathy,  it  must  rely  on  a  body  of  judges 
who  appeal  to  law  and  reason,  and  who  have  discarded 
the  powerful  check  of  personal  responsibility  and  per- 
sonal reward.  Instead  of  choosing  individuals  from 
society  to  form  a  more  or  less  cohesive  sect,  the  eu- 
genists  must  constrain  all  individuals  to  forsake  their 
personal  desires  and  attempt  to  bind  these  hetero- 
geneous units  into  a  homogeneous  race.  And  who  are 
intellectually  wise  enough  to  be  the  arbiters  of  fate? 
The  clinging  of  man  to  the  idea  of  corporal  manifesta- 
tions of  divinity  is  a  confession  of  the  impotence  of 
man  to  grasp  the  problem  of  humanity.  Huxley  stated 
this  difficulty  unanswerably  long  before  eugenics  came 
to  life.  He,  the  evolutionist  and  biologist,  warns  us: 
"  I  doubt  whether  even  the  keenest  judge  of  character, 
if  he  had  before  him  a  hundred  boys  and  girls  under 


250         THE  LIMITATIONS  OF  SCIENCE 

fourteen,  could  pick  out,  with  the  least  chance  of  suc- 
cess, those  who  should  be  kept,  as  certain  to  be  service- 
able members  of  the  polity,  and  those  who  should  be 
chloroformed,  as  equally  sure  to  be  stupid,  idle,  or 
vicious.  The  *  points '  of  a  good  or  bad  citizen  are 
really  far  harder  to  discern  than  those  of  a  puppy  or  a 
short-horn  calf;  many  do  not  show  themselves  before 
the  practical  difficulties  of  life  stimulate  manhood  to 
full  assertion.  The  evil  stock,  if  it  be  one,  has  had  time 
to  multiply,  and  selection  is  nullified." 

Instead  of  a  sober  and  careful  study,  with  a  full 
realization  of  the  almost  hopeless  difficulties  of  the 
problem,  we  have  a  number  of  people,  mostly  of  a  very 
restricted  outlook,  who  say  with  conviction  that  man  is 
mentally  defective,  man  is  diseased,  man  is  criminal. 
And  they  say  vaguely,  these  misfortunes  must  be 
stopped.  But  how  is  any  one  of  these  to  be  remedied 
or  how  are  we  to  weigh  or  balance  them  ?  A  man  may 
be  a  criminal  and  otherwise  a  perfect  physical  creat- 
ure; a  man  may  be  diseased  and  yet  be  intellectually 
and  morally  a  giant ;  in  fact,  Lombroso  claims  that  all 
those  we  most  reverence  for  morality  or  intellect  were 
diseased  and  quite  unfit  to  be  progenitors  of  the  race. 
And  while  this  doctrine  of  Lombroso,  that  intellectual 
and  moral  genius  is  a  symptom  of  physical  degeneracy, 
is  a  monstrous  falsehood,  yet  it  is  certain  that  those 
who  possess  great  powers  themselves  frequently  do  not 
transmit  their  excellent  qualities.  And  these  are  only 


THE  ARBITER  OF  ETHICS  251 

the  simplest  attributes  of  a  good  citizen  to  be  con- 
sidered. 

So  far  eugenics  has  limited  itself  to  a  trite  formula 
that  only  the  fit  should  be  permitted  to  have  children. 
This  battle-cry  has  been  sung  loudly  and  it  has  gath- 
ered together  a  motley  band  who  would  interfere  with 
the  laws  of  nature  and  reform  civilization  overnight. 
They  have  no  clear  idea  who  are  the  fit  or  how  the  unfit 
are  to  be  restrained.  They  busy  themselves  collecting 
statistics,  but  for  the  most  part  these  are  undigested, 
or  are  drawn  from  questionnaires  scattered  broadcast 
and  inviting  inaccuracy,  and  frequently  they  are  not 
even  honest.  Books  also  are  written  and  as  an  exposi- 
tion of  an  ethical  system  they  give  the  impression  that 
the  writers'  loftiest  aim  is  to  turn  the  human  race 
into  a  stock-breeding  farm.  The  chief  argument  and 
the  complaint  is  that  men  can  breed  cattle,  dogs,  and 
plants  eugenically  but  not  themselves.  But  what  an 
absurd  attitude  this  is !  The  breeder  of  dogs  and  cattle 
stands  in  a  relation  to  them  much  as  a  god  would  to 
us.  Dogs  and  cattle  are  bred  to  bring  into  prominence 
some  trait  which  will  suit  the  purpose  or  pleasure  of 
their  master,  not  of  their  own.  No  one  supposes  that 
the  monstrous  nose  of  the  pug  dog  or  the  inflamed  liver 
of  the  Strassburg  goose  was  developed  with  any  regard 
to  those  unfortunate  animals.  The  whole  point  has 
been  missed.  Man  cannot  be  bred  like  animals  be- 
cause he  has  no  apparent  master.  If  we  could  be 


252         THE  LIMITATIONS  OF  SCIENCE 

content  to  believe  that  the  destiny  of  man  is  under 
divine  control,  we  can  have  hope;  and  if  it  is  left  to 
the  rough  methods  of  nature,  which  sooner  or  later 
blot  out  the  degenerate  and  the  weakling,  there  is 
some  possibility  of  achievement. 

In  spite  of  much  noise  about  the  science  of  eugenics, 
the  eugenists  know  that  at  most  it  is  but  a  police  regu- 
lation. Society  has  always  assumed  the  right  to  pro- 
tect itself  by  isolating  or  by  punishing,  even  with  death, 
those  it  considers  dangerous  to  its  stability.  The  eu- 
genists are  advocating  the  same  thing  and  have  so  far 
limited  their  efforts  to  prevent  children  from  criminals, 
imbeciles,  drunkards,  and  syphilitics.  The  methods  of 
society  to  accomplish  this  safeguard  have  been  crude, 
but  they  have  been  sufficiently  effective  to  prevent  any 
notable  deterioration  of  the  race,  and  it  is  safe  to  say 
there  has  been  improvement.  If  the  eugenists  would 
try  to  improve  the  methods  of  the  past  to  some  extent, 
something  might  be  done.  But  there  is  reason  for  be- 
lieving that  even  this  good  is  likely  to  be  stifled  by 
the  outcries  and  rash  heedlessness  of  the  overzealous. 

To  prevent  the  strains  of  disease,  imbecility,  and 
criminality  from  continuing  in  the  race,  we  now  have 
the  proposed  surgical  remedy  of  vasectomy.  As  an 
efficient  preventative  it  must  be  a  failure.  No  society 
would  countenance  such  an  operation  except  for  cases 
of  hopeless  degeneracy.  While  it  might  reduce  some- 
what the  number  of  degenerate  offspring,  we  would 


THE  ARBITER  OF  ETHICS  253 

still  have  the  children  of  the  less  degenerate,  who 
may  inherit  the  weakness  of  the  parent  in  an  intensified 
form.  No  good  arguments  can  be  given  against  the 
more  humane  method  of  the  separation  of  sexes  in 
institutions.  This  method  requires  merely  a  reform 
in  such  institutions  as  already  exist  in  order  that  their 
inmates  may  be  provided  with  as  free  and  useful  life  as 
is  possible.  The  argument  is  frequently  given  that  the 
cost  of  this  method  is  great.  But  a  strong  and  vigorous 
community  may  well  blush  at  such  a  motive;  certainly 
the  care  of  its  unfortunates  is  a  solemn  duty  and  it 
should  be  undertaken  with  as  much  solicitude  as  a  man 
would  shield  a  weakling  child.  And  as  for  the  plea 
that,  after  this  operation,  the  individual  loses  only  the 
power  and  not  the  desire  to  procreate,  it  strikes  one  as 
simply  disgusting.  Is  it  not  giving  a  license  to  the 
degenerate  and  to  the  man  of  loose  morals  to  be  as  foul 
as  he  pleases  if  only  his  sins  end  with  himself?  It 
would  be  far  more  manly,  if  the  plan  of  isolation  can- 
not succeed,  to  put  degenerate  children  and  adults  to 
death  and  at  least  preserve  some  self-respect  for  the 
dignity  of  human  life. 

Another  plan  proposed  to  promote  eugenics  is  to 
rely  on  the  legislator  and  the  clergy  to  prohibit  mar- 
riage, unless  the  contracting  parties  show  certificates 
of  fitness  from  a  physician.  Without  the  least  knowl- 
edge of  what  effect  such  a  regulation  would  have,  the 
state  of  Wisconsin  has  recently  passed  a  law  of  this 


254         THE  LIMITATIONS  OF  SCIENCE 

character.  The  result  so  far  has  been  ridicule  and  a 
marked  decrease  in  marriages.  The  absolute  inability 
to  carry  out  the  purpose  of  such  a  law  does  not  seem  to 
have  occurred  to  its  promoters.  If  it  were  enforced 
over  a  wide  area,  the  youth  would  certainly  dispense 
with  the  ceremony  of  marriage  rather  than  to  debase 
their  ideals  of  love.  And  one  can  imagine  the  con- 
sternation of  physicians  if  they  were  forced  to  decide 
when  people  were  fit  to  marry.  Very  few  of  them 
know  anything  about  the  laws  of  heredity,  and  those 
that  do  know  the  laws  of  heredity  also  know  that  they 
are  so  complex  and  so  obscure  that  only  a  few  extreme 
cases  can  be  trusted.  As  Huxley  said,  the  points  of 
a  good  citizen  are  more  difficult  than  those  of  a  puppy 
or  a  short-horn  calf. 

A  third  class  of  eugenists  consists  mostly  of  the 
hysterical  element  of  the  social  workers  who  sob  over 
the  sins  of  society  and  sob  over  the  innate  purity  of 
the  harlot,  who  weep  over  the  heartlessness  of  the  law- 
abiding  and  weep  over  the  innate  nobility  of  the  crimi- 
nal. So  far  as  one  can  make  out  from  their  incoherent 
utterances,  they  wish  to  put  all  the  sins  of  the  individual 
on  society,  without  comprehending  that  society  is  a  col- 
lection of  individuals.  Whatever  good  they  may  ac- 
complish, no  one  in  the  least  conversant  with  science 
will  concede  that  they  are  advancing  an  ethics  in  con- 
formity with  scientific  methods;  for  if  science  makes 
any  one  thing  clear,  it  is  that  the  actions  of  the  indi- 


THE  ARBITER  OF  ETHICS  255 

vidual  must  bring  their  reactions  also  on  the  same  in- 
dividual. 

Now  it  seems  to  me  that  in  eugenics  of  the  simplest 
type  there  is  a  possible  good.  If  the  advocates  of  good 
breeding,  and  everyone  is  that  to  some  extent,  will 
work  quietly  and  systematically  on  the  problems  of 
heredity;  if  they  will  try  to  find  the  effects  of  criminal- 
ity and  of  disease  on  posterity,  we  shall  then  have  some 
reliable  facts  to  work  on.  We  may  then  hope  to  ac- 
complish some  more  decent  plan  of  isolating  the  worst 
of  such  cases  than  we  have  now.  And  we  are  sure  of 
the  help  of  society  itself,  for  we  know  that  the  human 
race  contains  in  itself  the  power  of  gradually  eradicat- 
ing defective  stock  from  the  simple  fact,  that  if  it  did 
not  possess  this  power,  it  would  have  hopelessly  de- 
generated long  ago.  But  this  natural  process  is  slow 
and  if  it  can  be  accelerated  and  guided,  eugenics  will 
be  valuable. 

There  are  many  of  these  patient  and  accurate  in- 
vestigators of  the  laws  of  heredity  but  there  are  also  un- 
fortunately others,  classed  professionally  as  eugenists, 
whose  methods  are  not  so  reliable.  From  their  bureaus 
issue  questionnaires  which  are  spread  broadcast.  The 
statistics  which  result  are  mostly  useless  and  often 
false,  as  they  are  given  by  untrained  people.  And 
they  are  especially  obnoxious  as  they  too  frequently 
make  a  direct  appeal  to  the  morbid.  Their  so-called 
laws  are  based  on  insufficient  evidence.  Apparently 


256         THE  LIMITATIONS  OF  SCIENCE 

the  only  two  examples  which  have  been  worked  out 
in  America  are  the  Jukes  and. the  Edwards  families. 
The  first  has  shown  itself  to  be  an  undesirable  and 
the  other  a  desirable  strain.  But  curiously  enough  the 
first  ancestress  in  America  of  each  of  these  families 
was  not  a  moral  woman.  It  is  sufficiently  easy  to  look 
back  and  decide  what  characteristics  proved  to  be  un- 
desirable, but  it  is  a  very  different  thing  to  look  for- 
ward and  determine  who  should  establish  a  family 
and  who  should  not.  Not  even  the  most  enthusiastic 
eugenists  can  hope  to  unravel  the  genealogies  of  more 
than  a  small  proportion  of  families.  And  it  would 
require  accurate  genealogies  of  many  families,  not 
only  of  successive  generations  but  also  of  the  char- 
acteristics of  its  members,  to  settle  whether  a  strain 
of  immorality  came  simply  from  an  excess  of  vitality 
or  was  the  result  of  degeneracy. 

If  eugenics  is  a  problem  too  complex  for  solution, 
its  companion,  euthenics,  is  an  example  of  trying  to 
assign  to  science  a  problem  it  has  no  means  of  solving. 
Science  knows  no  method  of  constraining  an  indi- 
vidual to  conduct  himself  so  as  to  further  the  exist- 
ence of  a  perfect  race.  The  greatest  difficulty  in  all 
ethical  systems  is  to  provide  an  efficient  check  on  the 
passions.  The  strongest  check  is  evidently  the  belief 
that  disaster  to  himself  will  result  from  disobedience 
of  the  laws  of  right  conduct.  And  yet  the  man  is  rare 
who  can  by  his  will  refrain  from  those  habits  and 


THE  ARBITER  OF  ETHICS  257 

passions  which  he  knows  to  be  injurious  to  him- 
self or  to  those  nearest  and  dearest  to  him.  What 
more  ineffective  system  of  ethics  could  be  imagined 
than  euthenics,  which  bases  its  claim  on  the  plea  that 
a  man  should  so  live  that  the  race  may  move  forward 
to  some  unknown  goal  of  perfection?  And  he  is  not 
even  to  have  the  satisfaction  of  seeing  the  progress  of 
the  race,  as  little  improvement  is  to  be  expected  for  a 
hundred  or  so  of  generations. 

The  average  man  is  too  busy  with  his  own  con- 
cerns even  to  consider  those  of  a  distant  posterity,  of 
whose  needs  he  can  know  nothing.  He  is  convinced 
that  future  generations  cannot  be  controlled  by  him  and 
that  they  must  solve  their  own  problems;  and  he  is 
also  conscious  that  he  is  not  altogether  degenerate 
although  he  is  the  result  of  a  long  line  of  careless  an- 
cestors, heedless  of  him  and  ignorant  of  eugenics  and 
euthenics.  However  traits  of  heredity  may  affect 
immediate  posterity,  it  must  be  recognized  as  a  general 
principle  that  the  race  has  attained  a  normal  develop- 
ment, which  can  change  but  slightly  and  very  slowly ; 
disease  and  vice  must  disappear  just  as  abnormal  excel- 
lences must  decay.  We  find  but  little  that  is  essentially 
different  in  the  moral  character  of  ourselves  and  that 
of  persons  who  formed  the  ancient  civilizations.  The 
eugenists  forget  that  the  great  majority  of  all  men,  and 
a  still  greater  majority  of  those  of  influence,  lead  for 
the  most  part  decent,  law-abiding  lives,  and  this  quiet 


258         THE  LIMITATIONS  OF  SCIENCE 

and  unobtrusive  power  of  example  is  far  more  potent 
for  righteousness  than  a  propaganda  led  by  enthusiasts. 

Side  by  side  with  the  doctrine  that  human  sympathy 
is  the  controlling  factor  of  ethics,  and  this  belief  is 
evidently  the  basis  of  eugenics,  there  has  always  per- 
sisted the  contrasted  doctrine  that  the  state  of  man  is 
one  of  warfare,  a  survival  of  the  fit.  This  school 
evidently  relies  on  a  law  of  natural  evolution  based 
on  the  motive  of  egotism.  It  is  thus  my  fourth  class 
of  naturalism. 

Of  all  those  who  have  advanced  this  motive  of 
egotism,  none  has  done  so  as  explicitly,  or  has  made  of 
it  so  complete  a  philosophy  as  Hobbes.  "  In  the  first 
place,"  he  says,  "  I  put  forth,  for  a  general  inclination 
of  all  mankind,  a  perpetual  and  restless  desire  of 
power  after  power,  that  ceaseth  only  in  death."  This 
is,  I  think,  the  direct  influence  of  science  unqualified 
by  character  and  piety.  It  is  not  my  purpose  to  follow 
this  doctrine  down  to  the  present  time  but  it  can  be 
shown  that  Nietzsche,  with  his  ideal  of  the  Superman, 
is  the  logical  successor  of  Hobbes.  Both  the  strength 
and  weakness  of  this  form  of  philosophy  have  been 
contrasted  in  a  recent  essay :  * 

"  Nietzsche  regarded  the  self-assertive  Superman 
as  a  true  reaction  against  the  prevalent  man  of  sym- 
pathy, and  as  a  cure  for  the  disease  of  the  age.  That 

*  Essay  on  Nietzsche.  By  Paul  Elmer  More.  Shelburne  Es- 
says; Eighth  Series. 


THE  ARBITER  OF  ETHICS  259 

much  of  Nietzsche's  protest  against  the  excesses  of 
humanitarianism  was  sound  and  well  directed,  I  for 
one  am  quite  ready  to  admit.  He  saw,  as  few  other 
men  of  our  day  have  seen,  the  danger  that  threatens 
true  progress  in  any  system  of  education  and  gov- 
ernment which  makes  the  advantage  of  the  ordinary 
rather  than  the  distinguished  man  its  first  object.  He 
saw  with  terrible  clearness  that  much  of  our  most  ad- 
mired art  is  not  art  at  all  in  the  higher  sense  of  the 
word,  but  an  appeal  to  morbid  sentimentality.  .  .  . 
But  the  cure  Nietzsche  proposed  for  these  evils  was  it- 
self a  part  of  the  malady.  The  Superman,  in  other 
words,  is  a  product  of  the  same  naturalism  which  pro- 
duced the  disease  it  would  counteract;  it  is  the  last  and 
most  violent  expression  of  the  egotism,  or  self-interest, 
which  Hume  and  all  his  followers  balanced  with  sym- 
pathy, as  the  two  springs  of  human  action." 

If  the  predominant  object  of  science  is  to  acquire 
power,  how  can  we  escape  the  conclusion  that  if  it 
should  become  the  arbiter  of  ethics,  society  would  tend 
to  a  condition  closer  to  the  ideals  of  Nietzsche  than  of 
sentimental  eugenics  ?  Can  we  look  with  complaisance 
on  the  unrestricted  development  of  either  of  these 
ideals?  Nietzsche  teaches  a  gospel  of  scientific  evolu- 
tion when  the  restraints  are  removed  from  the  free 
exercise  of  self-interest.  The  gospel  of  the  Superman, 
when  transferred  to  the  ambitions  of  a  nation,  as  has 
been  done  by  Treitschke,  shows  its  results  in  that  doc- 


26o         THE  LIMITATIONS  OF  SCIENCE 

trine  of  necessity  of  the  Germans  which  has  plunged 
Europe  into  war.  No  individual  and  no  nation  can 
believe  for  long  that  in  him  or  in  it  rest  the  culture 
and  the  power  of  the  world  without  resorting  ulti- 
mately to  the  arbitrament  of  force  to  overcome  opposi- 
tion. And  on  the  other  hand,  the  ideal  of  a  world 
governed  by  human  evolution  and  depending  on 
brotherly  love — a  world  under  a  banner  floating  from 
a  Peace  Palace  of  The  Hague — is  a  dream  of  sentimen- 
tality. And  yet,  one  or  the  other  seems  to  me  the  goal 
of  eugenical  righteousness.  But  because  science  is  not 
concerned  primarily  with  problems  of  character,  it 
does  not  follow  that  its  pursuit  does  not  promote  char- 
acter. We  certainly  enrich  the  character  by  the  larger 
acquisition  of  power  which  results  from  the  modifying 
and  dominating  of  our  environment.  This  is  true,  if 
side  by  side  with  increased  power  to  do  things,  we 
also  learn  to  use  it  for  the  benefit  of  humanity;  that 
is,  when  it  is  regulated  according  to  the  inner  check  of 
piety,  as  taught  by  those  in  whom  we  recognize  the 
mysterious  power  of  righteousness. 

If  I  have  made  myself  clear,  the  limitations  of  sci- 
ence are  due  solely  to  the  fact  that  there  are,  in  addi- 
tion to  material  forces,  others  of  an  essentially  dif- 
ferent kind  which  may  be  called,  for  lack  of  a  better 
name,  spiritual  powers.  And  so  long  as  men  of  sci- 
ence restrict  their  endeavor  to  the  world  of  material 
substance  and  material  force,  they  will  find  that  their 


THE  ARBITER  OF  ETHICS  261 

field  is  practically  without  limits,  so  vast  and  so  numer- 
ous are  the  problems  to  be  solved.  And  it  should  dis- 
tress no  one  to  discover  that  there  are  other  fields  of 
knowledge  in  which  science  is  not  concerned;  on  the 
contrary,  the  fact  that  the  range  of  science  is  limited 
should  encourage  us  to  greater  hopes,  because  our 
freedom  of  action  is  still  far  greater  than  our  powers 
of  accomplishment.  After  centuries  of  effort,  the 
ocean  of  the  unknown  lies  before  us  unexplored. 


INDEX 


Abstractive  and  hypothetical 
methods,  13;  outlined  by 
Rankine,  20. 

Action  at  a  distance,  84,  134- 

Ampere,  abstractive  method, 
190. 

Aristotle,  continuity,  77;  dic- 
tator of  Greek  and  medieval 
science,  230;  spirit  of  Greek 
science,  231;  ideas  as  logic, 
231. 

Astronomy,  its  relation  to  hy- 
pothesis, 76. 

Atomic,  Kelvin's  models,  36, 
190;  nature  of  electricity, 
138. 

Atomic  theory,  defined,  8;  its 
axioms,  n;  failure,  24;  not 
an  aid  to  discovery,  33;  in- 
adequacy of,  44;  modern  and 
classic,  49;  its  nature,  73; 
its  philosophical  weakness, 
119;  its  value,  130. 

Atoms,  nature  of,  10;  Lar- 
mor's  definition,  26,  49;  nec- 
essary attributes,  44;  sub- 
divided, 44;  modern  concep- 
tions, 129. 

Axioms,  of  atomic  theories, 
1 1 ;  see  Postulates. 

Bacon,  Fr.,  natural  philosophy, 
121 ;  province  of  mathemat- 
ics, 142;  on  the  sources  of 
knowledge,  233 ;  on  the  ex- 
tent and  limit  of  science, 
234- 

Biology,  as  the  basis  of  ethics, 
236. 

Bolingbroke,  Lord,  critique  of 
Descartes's  cosmogony,  104, 

144- 

Boscovich,  atomic  theory,  8. 

Bradley,  discovery  of  the  aber- 
ration of  light,  19. 


Browne,  Sir  Thomas,  nature 
of  electricity,  108. 

Campbell,  Norman,  division  of 
past  and  present  science,  39. 

Celestial  matter,  nature  of,  99. 

Character,  not  the  aim  of  sci- 
ence, 229. 

Clifford,  W.  K,  plurality  of 
ethers,  n. 

Cohesion,  cause  of,  Descartes, 
92;  Larmor,  127. 

Continuity  and  discontinuity 
of  matter,  contrasted,  3,  119; 
as  a  dualistic  principle,  40, 
44;  ideas  on,  77;  its  history, 
77;  conflict  between,  78;  in- 
ability to  decide  between, 
143- 

Cosmogony,  of  Laplace  and 
Lagrange,  7;  Larmor's,  47; 
requirements  for  a  scientific, 
72;  nebular  hypothesis,  74; 
as  a  scientific  convenience, 
80;  Descartes's,  82  et  seq.; 
revealed  and  natural,  240. 

Coulomb,  nature  of  electricity, 
153- 

d'Alembert,  laws  of  motion,  6. 

Dalton,  atomic  theory,  33. 

Darwin,  law  of  evolution,  226, 
238. 

Democritus,  atomic  theory,  8, 
73. 

Descartes,  influence  on  science, 
3,  5,  39,  40,  67,  101,  142,  224; 
theory  of  matter,  40;  the 
plenum,  40,  78;  example  of 
hypothetical  method,  70;  ex- 
ponent of  continuity  of  mat- 
ter, 78;  scientific  principles, 
79;  revelation,  80;  attributes 
of  substance,  82;  action  at 
a  distance,  84;  laws  of  mo- 


263 


264 


INDEX 


tion  and  impact,  85;  classi- 
fication of  matter,  86;  vor- 
tices, 89 ;  cohesion,  92 ;  light, 
92;  heat,  95;  the  earth,  96; 
his  consistency  of  thought, 
98;  critique  of  his  cosmog- 
ony, 101,  Bolingbroke's 
opinion,  104;  nature  of  elec- 
tricity, 107;  space  as  sub- 
stance, 236. 

pufay,  fluid  theory  of  elec- 
tricity, 25. 

Duhem,  on  science  of  ener- 
getics, 22;  on  theories  of 
physics,  37. 

Egoism,  as  a  scientific  system 
of  ethics,  258. 

Einstein,  definition  of  space, 
109,  127,  153;  electricity  and 
energy  as  entities,  in. 

Einstein's  Principle  of  Rela- 
tivity, to  harmonize  modern 
and  Newtonian  mechanics, 
164 ;  its  postulates,  165  ;  meas- 
ure of  time,  167;  measure 
of  length,  169;  variability  of 
mass,  172;  mass  and  energy, 
172;  its  postulates,  174;  re- 
striction of  the  relativity  of 
motion,  175;  absolute  veloc- 
ity of  light,  177;  velocity  of 
sound  and  light,  an  illustra- 
tion, 182;  atomic  nature  of 
electricity,  184;  logical  but 
false,  184. 

Electricity,  an  entity,  42,  51, 
63,  65,  107,  no,  184;  the 
basis  of  mechanics,  158. 

Electrons,  nature  of,  55,  60, 
131,  135,  138. 

Energetics,  definition,  n,  20; 
value  of,  24. 

Energy,  the  basis  of  science, 
22;  conservation  of,  120,  128; 
classification,  122,  133. 

Ether,  a  mechanical  link,  10 ; 
need  for  more  than  one,  u; 
and  matter,  42;  its  prop- 
erties, 43;  elastic-solid  and 
electromagnetic,  52;  massive, 
109;  recent  ideas  of,  109;  a 


confession  of  ignorance,  125 ; 
a  plenum,  126;  a  new  con- 
ception of  the,  162;  a  con- 
venience only,  198;  as  a 
reality,  202 ;  as  the  explana- 
tion of  matter,  203;  the  re- 
ductio  ad  absurdum,  204; 
Lodge's  definition,  208;  as  a 
psychic  medium,  208;  as  a 
quasi-deity,  209. 

Ethereal,  see  Vortices. 

Ethics,  present  perplexity,  213; 
science  as  the  basis  of,  214; 
lack  of  criticism  of  sci- 
entists, 215;  effect  of  hy- 
pothesis on,  225;  material- 
ism, 233  ;  atheism,  233  ;  sys- 
tem of  Hobbes,  235;  science, 
the  guide  to  conduct,  237 ; 
law  of  evolution  not  eth- 
ical, 238 ;  evolution  and, 
241 ;  classification  of  natural- 
ism, 243;  egoism,  258;  rela- 
tion of  science  to,  260. 

Eugenics,  as  a  science,  245;  as 
a  system  of  ethics,  249;  as 
a  police  regulation,  252; 
under  guidance  of  physi- 
cians, 252;  under  guidance 
of  legislators  and  the  clergy, 
253;  under  the  social  work- 
ers, 254;  lack  of  influence, 
257- 

Eugenist,  defined,  246. 

Euthenics,  defined,  245;  its 
failure,  256. 

Evolution,  as  a  law,  116;  so- 
cial, 212;  discussed,  237;  its 
causes,  239;  natural  and  re- 
stricted, 241 ;  spiritual,  four 
types  of,  243. 

Experience,  the  basis  of  sci- 
ence, 233. 

Experimentum  crucis,  18. 

Fallacies,  in  Descartes's  sys- 
tem, 98. 

Faraday,  the  duty  of  science, 

107;  theory  of  electricity, 

108;  effect  of  dielectrics, 

160;  nature  of  the  ether, 
161. 


INDEX 


265 


Fire,     Descartes's     conception 

of,  90. 

Fiske,  John,  naturalism,  237. 
FitzGerald-Lorentz,    effect    of 

motion  on  matter,   160. 
Fizeau,  the  velocity  of  light  in 

moving  media,  177- 
Force,  as  the  basis  of  science, 

118. 
Foucault,   velocity   of   light  in 

transparent  media,  19. 
Franklin,    Benj.,    fluid    theory 

of  electricity,  25. 

Galileo,  on  sensation  as  the 
postulate  of  science,  32; 
founder  of  experimental  sci- 
ence, 39,  187;  classical  me- 
chanics, 142. 

Gassendi,  atomic  theory,  8,  85. 

Genealogies,  eugenics,  255. 

Generalization,  a  necessity,  194. 

Geometry,  its  postulates  com- 
pared with  those  'of  experi- 
mental science,  12 ;  the  basis 
of  science,  79. 

Goethe,  restraint  in  science, 
58. 

Guericke,  von,  theory  of  elec- 
tricity, 1 08. 

Hannequin,  atomic  theory,  I ; 
definition  of  mechanics,  118. 

Heat,  Descartes's  hypothesis, 
95- 

Helmholtz,  von,  conservation 
of  energy,  86;  vortex  rings, 
131 ;  stagnant  ether,  161. 

Heraclitus,  continuity  of  mat- 
ter, 77. 

Hertz,  H.,  opinion  of  Max- 
well's equations,  37 ;  electro- 
magnetic waves,  160. 

Histories  of  science,  their  de- 
ficiencies, 217. 

Hobbes,  on  the  sensations,  233, 
234 ;  metaphysical  system, 
235;  on  the  barometer,  236; 
egotism  of  mankind,  258. 

Hume,  on  the  sensations,  233; 
egotism  and  sympathy,  259. 

Huxley,  on  evolution,  241 ;  on 
eugenical  selection,  249. 


Huygens,  atomic  theory,  8,  40 ; 
theory  of  light,  19;  correc- 
tion of  laws  of  impact  and 
motion,  86. 

Hypothesis,  its  danger,  16 ; 
elimination  not  desirable,  37 ; 
utility  of,  42;  apology  for, 
57 ;  not  an  indifferent  sub- 
ject, 59;  Descartes's,  the 
most  complete,  98;  good  and 
bad  aspects,  103;  Boling- 
broke  on,  104 ;  and  symbol- 
ism, no;  a  tentative  hypoth- 
esis of  electricity,  140;  its 
value,  144;  effect  on  society, 
192;  as  generalization,  195; 
Poincare's  classification,  200; 
and  ethics,  225. 

Hypothetical  method,  13;  its 
deceptions,  70. 

Idolatry  of  scientists,  209. 
Impact,  Descartes's  laws,  85. 

Johnson,  Samuel,  reality  of 
matter,  206. 

Kant,  axioms  of  mechanics,  6; 
nebular  hypothesis,  74;  space 
and  time,  148. 

Kaufmann,  variation  of  mass 
with  velocity,  132,  137. 

Kelvin,  Lord  (Sir  Wm.  Thom- 
son), models  of  atoms,  36, 
190;  theory  of  vortex  atoms, 
41,  48,  131 ;  size  of  atoms, 
44;  origin  of  life,  117; 
quantitative  measurements, 
145. 

Lagrange,  axioms  of  mechan- 
ics, 6;  equilibrium  of  bodies, 
6;  Mecanique  analytique,  7; 
no  criterion  for  truth,  18. 

Laplace,  Systeme  du  monde,  7 ; 
materialistic  attitude,  8,  212; 
his  mechanistic  theory,  9; 
nebular  hypothesis,  74;  ve- 
locity of  propagation  of 
gravitational  energy,  118;  on 
the  inductive  method,  232. 

Larmor,  Sir  Joseph,  properties 
of  the  ether,  19,  53,  126; 


266 


INDEX 


corpuscular  theory  of  mat- 
ter, 26,  27,  41,  42,  44,  no; 
value  of  speculative  hypoth- 
esis, 43;  continuity  of  mat- 
ter, 46;  his  hypothesis  does 
not  avoid  former  difficulties, 
50;  divisibility  of  matter, 
119;  definition  of  ether,  126; 
electrical  theory  of  mechan- 
ics, 127;  definition  of  the 
atom,  129. 

Laws,  difference  between  hy- 
pothesis and,  104;  continuity, 
causal,  115. 

Leibnitz,  invention  of  the  cal- 
culus, 5. 

Length,  a  function  of  motion, 
169. 

Lewis,  G.  N.,  confusion  of 
fact  and  fiction,  112. 

Light,  theories  of,  19;  Des- 
cartes's  hypothesis,  92;  its 
velocity,  an  absolute  con- 
stant, 165 ;  its  ^  velocity  in 
vacuous  and  in  occupied 
space,  177;  its  velocity  not  a 
maximum,  182. 

Limits  of  science,  113. 

Locke,  on  the  sensations,  233. 

Lodge,  Sir  Oliver,  the  ether 
as  a  medium  for  psychic 
phenomena,  24;  ether  mas- 
sive, no,  153;  presidential 
address  on  Continuity,  193; 
his  scientific  credulity,  194; 
his  scientific  confusion,  207 ; 
his  ideas  of  the  ether  as  om- 
nipotent and  omniscient, 
208;  as  a  quasi-deity,  208; 
as  a  soul-body,  209;  his 
speculations  not  logical,  209; 
war  between  science  and  the- 
ology, 210;  as  an  example 
of  scientific  dogmatism,  210. 

Lombroso,  the  imperfection  of 
the  genius,  250. 

Lorentz,  H.  A.,  his  corpus- 
cular theory  of  matter,  26, 
28,  41,  55,  no,  130,  144; 
properties  of  the  ether,  56; 
apology  for  the  hypothetical 
method,  57;  ethereal  stresses 


not    realities,    109;    contrac- 
tion   of    matter,    160;    ether 
stresses,  161. 
Lucretius,  atomic  theory,  73. 

Mach,  Ernst,  science  of  ener- 
getics, 22. 

Mass,  as  an  attribute  of  elec- 
tricity, 64,  117,  135,  171;  as 
a  fundamental  unit,  145,  148, 
153 ;  Newton's  conception, 
155;  as  dependent  on  en- 
ergy, 172. 

Mathematics,  as  a  scientific 
language,  71;  its  value,  150; 
a  paradox,  151 ;  not  subject 
to  the  restrictions  of  science, 
185. 

Matter,  real  and  hypothetical, 
17;  continuous  or  discontin- 
uous, 40,  44;  modern  defini- 
tions, 50;  identity  of  space 
and,  82;  fundamental  attri- 
bute of,  82;  three  primordial 
kinds,  88;  terrestrial,  96; 
confusion  with  electricity, 
no;  its  divisibility,  119; 
true  and  sensible,  120;  as 
Ding  an  sich,  148;  our  con- 
cept of,  150;  as  an  ethereal 
strain,  161 ;  Poincare's  defini- 
tion, 205. 

Maxwell,  J.  C,  theory  of  light, 
19,  160;  theory  of  electrifi- 
cation, 25,  108;  discredit  of 
vortex  theory,  48,  131 ;  ori- 
gin of  life,  117;  nature  of 
the  ether,  161. 

Mechanical,  rise  of  principles, 
5 ;  theories  have  no  criterion 
of  truth,  18;  models  do  not 
lead  to  discoveries,  37;  the- 
ories, their  weakness,  62. 

Mechanics,  dominance  over 
science,  4;  axioms,  6;  its 
metaphysical  basis,  12;  the 
only  complete  theory,  13;  its 
failure  ^as  a  method,  146; 
Newtonian,  154;  the  new, 
159- 

Mechanistic  idea  of  the  uni- 
verse, 8. 


INDEX 


267 


Metaphysical  theory,  Larmor's, 
27;  Lorentz's,  28;  influence 
on  thought,  28. 

Metaphysics,    definition,    i. 

Method,  of  physics  a  model, 
3;  abstractive  and  hypo- 
thetical, 13;  Rankine's,  20; 
the  author's  outline,  115; 
Laplace's  opinion,  232. 

Michelet,  69. 

Michelson,  A.  A.,  ether  drift, 
159,  179;  velocity  of  light  in 
moving  media,  177. 

Minkowski,  four  dimensional 
space,  in. 

Models,  for  radiation,  123;  see 
Atoms. 

Moral  influence  of  science, 
213. 

More,  L.  T.,  outline  of  a  sci- 
entific method,  115;  on  ether 
stresses,  161. 

More,  P.  E.,  'on  Nietzsche  and 
the  doctrine  of  egoism,  258. 

Morley,  Edward,  on  ether 
drift,  159,  179. 

Motion,  real  and  hypothetical, 
152. 

Naturalism,  as  social  evolu- 
tion, 243. 

Nebular  hypothesis,   74. 

Newton,  on  hypothesis,  title 
page;  calculus,  5;  law  of 
gravitation,  6,  21,  its  appli- 
cation to  atoms,  7,  40,  74; 
hypothesis  of  light,  19,  21, 
226;  action  and  reaction,  115; 
classical  mechanics,  142,  154 
et  seq.;  on  mass,  155;  re- 
placing Kepler's  laws,  203. 

Nietzsche,  Fr.,  reaction  against 
humanitarianism,  258. 

Occult,  substances  and  forces, 

Organon  of  Aristotle,  the  text 
for  Greek  and  medieval  sci- 
ence, 230. 

Organum  Novum  of  Bacon, 
the  authority  for  modern 
science,  231. 


Ostwald,  W.,  science  of  ener- 
getics, 22. 


Peripatetic  school,  231. 

Philosophy,  metaphysical 
teaching  of  scientific,  i,  221 ; 
of  Greeks  characterized  by 
Bacon,  231;  of  Hobbes,  234; 
scientific,  236  et  seq. 

Physical  theory,  nature  of,  12; 
aims  of,  37;  originators  of, 
4i. 

Physics,  has  best  scientific 
method,  2;  relation  to  meta- 
physics, 3;  dates  from,  39. 

Planck,  Max,  quantum  theory 
of  discontinuity,  119;  on 
principle  of  relativity,  165. 

Plato,  the  world  as  idea,  231; 
and  eugenics,  248. 

Plenum,  40;  Larmor's  46; 
Descartes's,  83. 

Poincare,  H.,  on  hypothesis  of 
ether,  59;  The  Foundations 
of  Science,  193;  as  a  skeptic, 
193 ;  on  the  scientific  method, 
194;  on  generalizations,  194; 
on  hypothesis  as  a  conveni- 
ence, 198;  classification  of 
hypotheses,  200;  the  new 
mechanics,  203;  the  func- 
tion of  science,  204;  defini- 
tion of  matter,  205,  229. 

Postulates  of  science,  their 
truth,  81 ;  extent,  as  a  fun- 
damental attribute,  82;  of 
Descartes,  85,  148;  'of  Ein- 
stein, 165;  of  the  new  me- 
chanics, 174 ;  their  sub- 
jectivity, 219. 

Power,  the  aim  of  science, 
214;  as  the  desire  of  man- 
kind, 258,  260. 

Primordial  space  and  time,  72, 
86. 

Principia  Naturae  of  Des- 
cartes, 79  et  seq. 

Principia  of  Newton,  title 
page,  155. 

Proclus,  science  as  mathemat- 
ics, 232. 


268 


INDEX 


Radiant  energy,  nature  of, 
122;  and  its  medium  of 
transmission,  123,  128. 

Rankine,  on  energetics,  1 1 ;  on 
physical  theories,  12;  out- 
line of  abstractive  and  hy- 
pothetical methods,  16,  21. 

Relativity,  Principle  of;  see 
Einstein. 

Relativity,  of  motion  and  posi- 
tion, 83;  Descartes's  doc- 
trine, 83;  of  knowledge, 
147;  of  mechanical  motions, 
175;  not  applicable  to  radi- 
ant energy,  175 ;  an  aca- 
demic question,  182;  limited 
to  hypothetical  cases,  184. 

Remusat,  C.  de,  Vie  de  Bacon, 
233- 

Renan,  Ernest,  science  as  sym- 
bol and  law,  2,  212;  social 
evolution,  212. 

Roentgen,  W.  C,  discovery  of 
X-rays,  38. 

Rutherford,  Sir  Ernest,  ex- 
perimental evidence  for  at- 
oms, 60;  theory  of  radio- 
activity, 63. 

Science,  as  a  guide,  2,  58;  its 
limits,  30,  113,  228;  cata- 
logue of,  151 ;  its  functions, 
187 ;  its  domination  of  mod- 
ern thought,  188;  its  dog- 
matism, 189;  lack  of  crit- 
icism, 189,  215;  as  a  meas- 
ure of  civilization,  215; 
overthrow  of  Aristotelian, 
230;  its  aim  to  acquire  power 
and  not  character,  229;  and 
ethics,  a  modern  combina- 
tion, 234;  its  ethical  bearing, 
259;  its  true  aim,  260. 

Scientific,  method,  i ;  cult,  35 ; 
and  religious  polemic,  35; 
skepticism  and  credulity, 
193;  dogmatism,  210;  eth- 
ics, feasibility  of,  214. 

Scientists,  effect  of  hypoth- 
esis on,  28;  German  school 
of,  206,  207;  education  of, 
223- 


Sensations,  not  criteria  of 
phenomena,  8. 

Sentiment,  as  the  basis  of  hy- 
pothesis, 105. 

Space,  and  matter,  83;  our 
concept  of,  148. 

Spencer,  Herbert,  evolution  as 
a  social  law,  212,  238. 

Superman,  as  the  contrast  to 
eugenics,  259. 

Symbolism,    the    end    of    hy- 
pothesis,   no;    of    the    new   / 
mechanics,  206. 

Tennyson,  Lord,  humanitari- 
anism,  237. 

Theology  and  science,  30,  35, 
58,  210. 

Theory,  need  at  present  time, 
3- 

Thomson,  Sir  J.  J.,  properties 
of  atom,  17;  theory  of  mat- 
ter, 41,  54,  129;  on  electricity, 
109 ;  mass  of  electron,  136 ; 
artificiality  of  his  hypoth- 
esis, 202. 

Time,  our  idea  of,  149;  meas- 
urement of,  167;  a  property 
of  soace,  168;  variability 
with  motion,  171 ;  Einstein's 
idea  of,  181. 

Transcendental  symbolism  of 
German  physicists,  206,  207. 

Treitschke,  doctrine  of  neces- 
sity, 259- 

Units,  of  measure,  118. 
Universe  as  a  machine,  9,  18, 
72,  185. 

Velocity  of  light,  its  signifi- 
cance in  the  modern  ether, 
179. 

Vortex,  Kelvin's  theory,  48; 
Descartes's  theory,  87. 

Wilson,  C  T.  R.,  mass  of  the 

electron,  136. 
Wordsworth,  William,  human- 

itarianism,  237. 


BERGSON'S  CREATIVE  EVOLUTION 

Translated  from  the  French  by  <Dr.  Arthur  SHifchett 
8th  printing,  $2.50  net,  by  mail  $2.67. 

"Bergson's  resources  in  the  way  of  erudition  are  remark- 
able, and  in  the  way  of  expression  they  are  simply  phe- 
nomenal. ...  If  anything  can  make  hard  things  easy  to 
follow  it  is  a  style  like  Bergson's.  It  is  a  miracle  and  he 
a  real  magician.  Open  Bergson  and  new  horizons  open 
on  every  page  you  read.  It  tells  of  reality  itself  instead 
of  reiterating  what  dusty-minded  professors  have  written 
about  what  other  previous  professors  have  thought.  Nothing 
in  Bergson  is  shopworn  or  at  second-hand." — William  James. 

"A  distinctive  and  trenchant  piece  of  dialectic.  .  .  .  Than 
its  entrance  upon  the  field  as  a  well-armed  and  militant 
philosophy  there  have  been  not  many  more  memorable  occur- 
ences  in  the  history  of  ideas." — Nation. 

"To  bring  out  in  an  adequate  manner  the  effect  which 
Bergson's  philsophy  has  on  those  who  are  attracted  by  it 
let  us  try  to  imagine  what  it  would  have  been  like  to  have 
lived  when  Kant  produced  his  'Critique  of  Pure  Reason.'  "— 
Hibbert  Journal 

"Creative  Evolution  is  destined,  I  believe,  to  mark  an 
epoch  in  the  history  of  modern  thought.  The  work  has  its 
root  in  modern  physical  science,  but  it  blooms  and  bears 
fruit  in  the  spirit  to  a  degree  quite  unprecedented.  .  .  . 
Bergson  is  a  new  star  in  the  intellectual  firmament  of  our 
day.  He  is  a  philosopher  upon  whom  the  spirits  of  both 
literature  and  science  have  descended.  In  his  great  work 
he  touches  the  materialism  of  science  to  finer  issues.  Prob- 
ably no  other  writer  of  our  time  has  possessed  in  the  same 
measure  the  three  gifts,  the  literary,  the  scientific,  and  the 
philosophical.  Bergson  is  a  kind  of  chastened  and  spirit- 
ualized Herbert  Spencer." — John  Burroughs  in  the  Atlantic 
Monthly. 

HENRY     HOLT     AND     COMPANY 

PUBLISHERS  NEW  YORK 


FIFTY   YEARS   OF   DARWINISM 

Comprising  the  eleven  addresses  in  honor  of  Charles  Darwin 
delivered  January,  1909,  before  the  American  Association 
for  the  Advancement  of  Science.  $2.00  net;  by  mail  $2.16. 

CONTENTS: — Introduction,  T.  C.  Chamberlin;  Fifty  Years  of  Darwin- 
ism, E.  B.  Poulton;  The  Theory  of  Natural  Selection  from  the  Stand- 
point of  Botany,  J.  M.  Coulter;  Isolation  as  a  Factor  in  Organic 
Evolution,  D.  S.  Jordan;  The  Cell  in  Relation  to  Heredity  and  Evo- 
lution, E.  B.  Wilson;  The  Direct  Influence  of  Environment,  D.  T. 
MacDougal;  The  Behavior  of  Unit-Characters  in  Heredity,  W.  E. 
Castle;  Mutation,  C.  B.  Davenport;  Adaptation,  C.  H.  Eigenmann; 
Darwin  and  Paleontology,  H.  F.  Osborn;  Evolution  and  Psychology, 
G.  Stanley  Hall. 

KELLOGG'S   DARWINISM  TO-DAY 

By  VERNON  L.  KELLOGG,  Professor  in  Stanford  University. 
$2.00  net;  by  mail  $2.16. 

A  simple  and  concise  discussion  for  the  educated  layman  of  present- 
day  scientific  criticism  of  the  Darwinian  selection  theories,  together 
with  concise  accounts  of  the  other  more  important  proposed  auxiliary 
and  alternative  theories  of  species-forming. 

Its  value  cannot  be  over-estimated.  A  book  the  student  must  have 
at  hand  at  all  times,  and  it  takes  the  place  of  a  whole  library.  No 
other  writer  has  attempted  to  gather  together  the  scattered  literature 
of  this  vast  subject,  and  none  has  subjected  this  literature  to  such 
uniformly  trenchant  and  uniformly  kindly  criticism.  An  investigator 
of  the  first  rank,  and  master  of  a  clear  and  forceful  literary  style. — 
President  D.  S.  Jordan  in  the  Dial. 


LOCY'S  BIOLOGY  AND   ITS  MAKERS 

By  WILLIAM  A.  LOCY,  Professor  in  Northwestern  University. 

$2.75  net;  by  mail  $2.88. 

An  untechnical  account  of  the  rise  and  progress  of  biology;  written 
around  the  lives  of  the  great  leaders,  with  bibliography  and  index. 
The  123  illustrations  include  portraits,  many  of  them  rare,  of  nearly 
all  the  founders  of  biology.  The  book  is  divided  into  two  parts, 
Part  I  dealing  with  the  sources  of  biological  ideas  except  those  of 
Organic  Evolution,  and  Part  II  devoting  itself  wholly  to  Evolution. 

It  is  entertainingly  written,  and  better  than  any  other  existing  single 
work  in  any  language,  gives  the  layman  a  clear  idea  of  the  scope 
and  development  of  the  broad  science  of  biology. — Dial. 


HENRY     HOLT     AND     COMPANY 

34  WEST  33D  STREET  NEW  YORK 


BOOKS    ON    SOCIAL    SCIENCE 

SOCIALISM  AND  DEMOCRACY  IN  EUROPE 

By  SAMUEL  P.  ORTH.  With  bibliography  and  "Programs" 
of  the  various  Socialist  parties.  $1.50  net. 

Traces  briefly  the  growth  of  the  Socialist  movement  in 
France,  Belgium,  Germany,  England,  and  attempts  to  determine 
the  relation  of  economic  and  political  Socialism  to  Democracy. 

MARXISM  VERSUS  SOCIALISM 

By  V.  G.  SIMKHOVITCH,  Professor  of  Political  Science,  Col- 
umbia University.  $1.50  net. 

A  thorough  and  intimate  account  of  all  the  intricate  theories, 
problems  and  difficulties  of  modern  Socialism. 

Professor  Simkhovitch  shows  us  that  the  economic  tendencies 
of  to-day  are  quite  different  from  what  Marx  expected  them  to 
be  and  that  Socialism  from  the  standpoint  of  Marx's  own 
theory  is  quite  impossible. 

WHY  WOMEN  ARE  SO 

By  MARY  ROBERTS  COOLIDGE.    $1.50  net. 

"A  fearless  discussion  of  the  modern  woman,  her  inheritance,  her 
present  and  her  more  promising  future.  The  eighteenth  and  nineteenth 
century  woman  is  keenly  analyzed  and  compared  with  the  highest  type 
of  woman  to-day." — A.  L.  A,  Booklist. 

A  MONTESSORI  MOTHER 

By  DOROTHY  CANFIELD  FISHER.  With  Illustrations.  $1.25  net. 

A  simple  untechnical  account  of  the  apparatus,  the  method 
of  its  application,  and  a  clear  statement  of  the  principles  un- 
derlying its  use. 

"Mrs.  Fisher's  book  is  the  best  we  have  seen  on  the  subject." — In- 
dependent. 

THE  SOCIALIST  MOVEMENT  (Home  University  Library) 

By  J.  RAMSAY  MACDONALD,  Chairman  of  the  British  Labor 
Party.  50  cents  net. 

Traces  the  development  of  Socialistic  theory,  practice,  and 
party  organization ;  with  a  summary  of  the  progress  of  Socialist 
parties  to  date  in  the  leading  nations. 

"Not  only  the  latest  authoritative  exposition  of  Socialism,  it  is  also 
:he  most  moderate,  restrained  and  winning  presentation  of  the  subject 
now  before  the  public." — San  Francisco  Argonaut. 


HENRY      HOLT      AND      COMPANY 
PUBLISHERS  (v'13)  NEW  YORK 


HEREDITY  IN  RELATION  TO  EUGENICS 

By  CHARLES  B.  DAVENPORT,  Director,  Department  of  Experi- 
mental Evolution,  Carnegie  Institution  of  Washington.  With 
diagrams.  8vo.  $2.00  net. 

Eugenics  treats  of  inborn,  inheritable  capacities  and  tenden- 
cies. Modern  heredity  explains  how  these  tendencies  get 
into  the  children  and  assists  young  persons  to  select  consorts 
so  as  to  have  a  sound  offspring.  The  book  tells  what  is 
known  of  the  inheritance  of  various  diseases  and  other  char- 
acteristics; it  discusses  the  origin  of  feeblemindedness,  its 
vast  social  consequences,  and  its  elimination ;  it  considers 
American  families,  the  part  they  have  played  in  history,  and 
the  proof  they  furnish  of  the  all-importance  of  "  blood." 

"One  of  the  foremost  authorities  .  .  .  tells  .  .  .  just  what  scientific 
investigation  has  established  and  how  far  it  is  possible  to  control  what 
the  ancients  accepted  as  inevitable.  .  .  .  The  scientific  student  of  hered- 
ity will  find  in  it  the  latest  developments  and  achievements  in  his  partic- 
ular province.  .  .  .  Nevertheless,  it  is  meant  more  for  the  intelligent 
general  reader,  who  will  be  able  to  read  it  ...  with  entire  compre- 
hension. .  .  .  Many  interesting  instances  that  illustrate  how  good  or 
bad  tendencies,  physical,  mental,  or  moral,  radiate  from  the  focal  point 
of  a  single  individual  or  family."— N.  Y.  Times  Review. 

THE  EVOLUTION  OF  ANIMAL  INTELLIGENCE 

By  S.  J.  HOLMES,  Professor  in  the  University  of  Wisconsin. 

With  illustrations  and  charts.     8vo.     $2.75  net. 

A  general  account  of  the  evolution  of  animal  behavior  from 
the  mollusk  and  crustacean  up  to  apes  and  monkeys.  The 
critical  point  of  the  transition  from  instinct  to  intelligence  re- 
ceives special  treatment.  One  of  America's  leading  scientific 
authors  who  saw  the  manuscript  before  publication  writes, 
"  Holmes's  is  the  best  of  the  lot,  and  on  the  whole  the  most 
interesting  because  it  gives  the  most  facts;  i.e.,  examples, 
illustrations,  incidents,  stories,  etc.  Holmes  is  immensely  well 
informed." 

PFUNGST'S  CLEVER  HANS 

By  OSKAR  PFUNGST.    Translated  by  CARL  L.  RAHN,  Fellow  in 
Psychology  in  the  University  of  Chicago.     I2mo.    $1.50. 
The  performances  of  Clever  Hans,  the  horse  of  Mr.  von 
Osten,  created  throughout  Germany  intense  excitement  and  a 
widespread,  overheated  discussion  of  animal  reason. 

"The  book  is  a  minute  and  careful  examination  of  the  facts  in  the 
case,  and  should  be  of  interest  to  psychologists  and  to  all  students  of 
the  intelligence  of  the  lower  animals"."— Spring-field  Republican. 


HENRY    HOLT    AND    COMPANY 

PUBLISHERS  NEW   YORK 


WORKS  IN   PHILOSOPHY  AND 
PSYCHOLOGY 

Aikins's  Principles  of  Logic. 

By  Herbert  Austin  Aikins,  Professor  of  Philosophy  in  Western 
Reserve  University.  x+489pp.  i2mo.  $1.50. 

Angell's  Psychology. 

By  James  Rowland  Angell,  Professor  of  Pyschology  in  the  Uni- 
versity of  Chicago.  i2mo.  $1.60. 

Baldwin's  Elements  of  Psychology. 

By  James  Mark  Baldwin,  Professor  in  Johns  Hopkins  University, 
xv  -j-  372  pp.  I2mo.  $i  .60. 

Baldwin's  Handbook  of  Psychology. 

By  James  Mark  Baldwin,  Professor  in  the  Johns  Hopkins  University. 
SENSLS  AND   INTELLECT,      xiv  +  343   pp.      Svo.      Revised   Edition. 

$2.00. 

FEELING  AND  WILL,     xii  +  394  pp.     Svo.     $2.00. 
Colegrove's  Memory. 

An  Inductive  Study.  By  F.  W.  Colegrove.  With  an  Introduc- 
tion by  G.  Stanley  Hall,  LL.D.  369  pp.  i2mo.  $1.50. 

Dewey  &  Tufts's  Ethics. 

By  John  Dewey,  Professor  in  Columbia  University,  and  James  H. 
Tufts,  Professor  in  the  University  of  Chicago.  (American  Science 

Series.)     618  pp.      121110.     $2.00. 

Falckenberg's  History  of  Modern  Philosophy. 

Nicolas  of  Cusa  to  the  Present  Time.  By  Richard  Falckenberg, 
Professor  in  the  University  of  Erlangen.  Translated,  with  the 
author's  co-operation,  by  A.  C  Armstrong,  Jr.,  Professor  of  Phi- 
losophy in  W  esleyari  University,  xvi  +  655  pp.  Svo.  $3.50. 

Hyde's  Practical  Ethics. 

By  William  De  Witt  Hyde,  President  of  Bowdoin  College,  xi  -f  208 
pp.  i6mo.  $1.00. 

James's  Principles  of  Psychology.     ADVANCED  COURSE. 

By  William  James,  Professor  of  Psychology  in  Harvard  University. 
Two  volumes.  Svo.  (American  Science  Series.)  $5.00. 

James's  Psychology.     BRIEFER  COURSE. 

By  William  James,  Professor  in  Harvard  University,     xiii  -f-  478  pp. 

I2mo.     (American  Science  Series.)    $1.60. 

James's  Talks  to  Teachers  on  Psychology. 

By  William  James,  Professor  in  Harvard  University,  author  of 
"Principles  of  Psychology."  xii +301  pp.  I2mo.  $1.50. 

Jastrow's  Chapters  in  Modern  Psychology. 

By  Joseph  Jastrow,  Professor  in  the  University  of  Wisconsin,  pn 
preparation.] 


NEW  BOOKS  ON  THE  LIVING  ISSUES  BY  LIVING 
MEN   AND  WOMEN 

The  Home  University  Library 

Cloth  Bound  50c  per  volume  net ;  by  mail  56c. 

Points  about  THE  HOME   UNIVERSITY  LIBRARY 

Every  volume  is  absolutely  new,  and  specially  written  for 
the  Library.  There  are  no  reprints. 

Every  volume  is  sold  separately.  Each  has  illustrations 
where  needed,  and  contains  a  Bibliography  as  an  aid  to 
further  study. 

Every  volume  is  written  by  a  recognized  authority  on  its 
subject,  and  the  Library  is  published  under  the  direction  of 
four  eminent  Anglo-Saxon  scholars  —  GILBERT  MURRAY,  of 
Oxford;  H.  A.  L.  FISHER,  of  Oxford;  J.  ARTHUR  THOMSON, 
of  Aberdeen;  and  Prof.  W.  T.  BREWSTER,  of  Columbia. 

Every  subject  is  of  living  and  permanent  interest.  These 
books  tell  whatever  is  most  important  and  interesting  about 
their  subjects. 

Each  volume  is  complete  and  independent;  but  the  series 
has  been  carefully  planned  as  a  whole  to  form  a  compre- 
hensive library  of  modern  knowledge  covering  the  chief  sub- 
jects in  History  and  Geography,  Literature  and  Art,  Science, 
Social  Science,  Philosophy,  and  Religion.  An  order  for  any 
volume  will  insure  receiving  announcements  of  future  issues. 

SOME  COMMENTS  ON  THE  SERIES  AS  A  WHOLE: 

"Excellent." — The  Outlook.     "Exceedingly  worth  while." — The  Nation. 

"The   excellence  of   these  books." — The   Dial. 

"So   large   a   proportion   with   marked   individuality." — New    York   Sun. 

VOLUMES  ON  PHILOSOPHY  AND  RELIGION  NOW  READY 

Problems  of  Philosophy  Missions 

By  BERTRAND  RUSSELL.  By  MRS.  CREIGHTON. 

Ethics  The  Literature  of  the  Old  Test- 
By  G.  E.  MOORE.  ament 

Buddhism:  By  GEORGE  F.  MOORE. 

A  Study  of  the  Buddhist  Norm.  Comparative  Religion 
By  MRS.  RHYS  DAVIDS,  M.  A.         By  J.  ESTLIN  CARPENTER. 

English  Sects  The  Making  of  the  New  Test. 

A  History  of  Nonconformity.  ament 

By  W.  B.  SELBIE.  By  B.  W.  BACON. 

HENRY     HOLT     AND     COMPANY 

34  WEST  33d  STREET  (in'13)  NEW  YORK 


RETURN     CIRCULATION  DEPARTMENT 

TO—  ^      202  Main  Library 

1593 

LOAN  PERIOD  1 
HOME  USE 

2 

3 

4 

5 

6 

ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 

Renewals  and  Recharges  may  be  made  4  days  prior  to  the  due  date. 

Books  may  be  Renewed  by  calling     642-3405. 

DUE  AS  STAMPED  BELOW 


MAY  #6  1992 

V    9WWm 

AUTO.  0*^G 

NW  27  W*1 

CIRCULATION 

WK13J993 

AUTPDISCCIRC  wt 

(14  '9?, 

UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
FORM  NO.  DD6  BERKELEY,  CA  94720 


U.C.  BERKELEY  LIBRARIES 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


